Dimitrov, S. I. Square-free numbers of the form \(x^2+y^2+z^2+z+1\) and \(x^2+y^2+z+1\). (English) Zbl 07820488 Math. Notes 114, No. 6, 1169-1183 (2023). MSC: 11N37 11L05 11N25 PDFBibTeX XMLCite \textit{S. I. Dimitrov}, Math. Notes 114, No. 6, 1169--1183 (2023; Zbl 07820488) Full Text: DOI
Chan, Tsz Ho On moments of gaps between consecutive square-free numbers. (English) Zbl 1528.11095 Mosc. J. Comb. Number Theory 12, No. 4, 287-295 (2023). MSC: 11N25 PDFBibTeX XMLCite \textit{T. H. Chan}, Mosc. J. Comb. Number Theory 12, No. 4, 287--295 (2023; Zbl 1528.11095) Full Text: DOI arXiv
Chen, Gongrui; Wang, Wenxiao On the \(r\)-free values of the polynomial \(x^2+y^2+z^2+k\). (English) Zbl 07729548 Czech. Math. J. 73, No. 3, 955-969 (2023). MSC: 11N25 11L05 11L40 PDFBibTeX XMLCite \textit{G. Chen} and \textit{W. Wang}, Czech. Math. J. 73, No. 3, 955--969 (2023; Zbl 07729548) Full Text: DOI arXiv
Chen, Bo On the consecutive square-free values of the polynomials \(x_1^2 + \cdots + x_k^2+1\), \(x_1^2 + \cdots + x_k^2+2\). (English) Zbl 1517.11123 Indian J. Pure Appl. Math. 54, No. 3, 743-756 (2023). MSC: 11N37 11L05 11N25 PDFBibTeX XMLCite \textit{B. Chen}, Indian J. Pure Appl. Math. 54, No. 3, 743--756 (2023; Zbl 1517.11123) Full Text: DOI
Dimitrov, Stoyan Ivanov Square-free values of \(n^2 + n + 1\). (English) Zbl 1514.11058 Georgian Math. J. 30, No. 3, 333-348 (2023). MSC: 11N32 11L05 11N25 PDFBibTeX XMLCite \textit{S. I. Dimitrov}, Georgian Math. J. 30, No. 3, 333--348 (2023; Zbl 1514.11058) Full Text: DOI arXiv
Srichan, Teerapat Square-free and square-full part of an integer. (English) Zbl 1511.11071 Asian-Eur. J. Math. 15, No. 12, Article ID 2250211, 14 p. (2022). Reviewer: Mehdi Hassani (Zanjan) MSC: 11L40 11N25 11N37 PDFBibTeX XMLCite \textit{T. Srichan}, Asian-Eur. J. Math. 15, No. 12, Article ID 2250211, 14 p. (2022; Zbl 1511.11071) Full Text: DOI
Bouderbala, Mihoub On a new arithmetic additive function related to the generalized divisors of an integer. (English) Zbl 1513.11162 Math. Montisnigri 55, 25-30 (2022). MSC: 11N37 PDFBibTeX XMLCite \textit{M. Bouderbala}, Math. Montisnigri 55, 25--30 (2022; Zbl 1513.11162) Full Text: DOI
Castillo, Marianela A dynamical characterization for monogenity at every level of some infinite \(2\)-towers. (English) Zbl 1506.11121 Can. Math. Bull. 65, No. 3, 806-814 (2022). MSC: 11N32 11R04 11R80 PDFBibTeX XMLCite \textit{M. Castillo}, Can. Math. Bull. 65, No. 3, 806--814 (2022; Zbl 1506.11121) Full Text: DOI
Puttasontiphot, Tippawan On a sequence attached to powerful numbers: an elementary proof. (English) Zbl 1513.11161 Int. J. Math. Comput. Sci. 17, No. 3, 1299-1303 (2022). MSC: 11N25 11N60 PDFBibTeX XMLCite \textit{T. Puttasontiphot}, Int. J. Math. Comput. Sci. 17, No. 3, 1299--1303 (2022; Zbl 1513.11161) Full Text: Link
Pimsert, Watcharapon; Thansri, Thorranin On the square-free and square-full solutions of polynomial congruences. (English) Zbl 1499.11012 Int. J. Math. Comput. Sci. 17, No. 1, 309-315 (2022). MSC: 11A07 11L40 11N25 PDFBibTeX XMLCite \textit{W. Pimsert} and \textit{T. Thansri}, Int. J. Math. Comput. Sci. 17, No. 1, 309--315 (2022; Zbl 1499.11012) Full Text: Link
Jing, Mengyao; Liu, Huaning Consecutive square-free numbers and square-free primitive roots. (English) Zbl 1489.11005 Int. J. Number Theory 18, No. 1, 205-226 (2022). Reviewer: Ramdin Mawia (Kolkata) MSC: 11A07 11N25 11L40 PDFBibTeX XMLCite \textit{M. Jing} and \textit{H. Liu}, Int. J. Number Theory 18, No. 1, 205--226 (2022; Zbl 1489.11005) Full Text: DOI
Zhang, Wei On squares in Piatetski-Shapiro sequences. (English) Zbl 1490.11035 Funct. Approximatio, Comment. Math. 65, No. 2, 227-236 (2021). Reviewer: Olivier Bordellès (Aiguilhe) MSC: 11B83 11K65 11L07 11L40 11N25 PDFBibTeX XMLCite \textit{W. Zhang}, Funct. Approximatio, Comment. Math. 65, No. 2, 227--236 (2021; Zbl 1490.11035) Full Text: DOI
Bhardwaj, Neer; Tran, Chieu-Minh The additive groups of \(\mathbb{Z}\) and \(\mathbb{Q}\) with predicates for being square-free. (English) Zbl 07457781 J. Symb. Log. 86, No. 4, 1324-1349 (2021). MSC: 03C65 03B25 03C10 03C64 PDFBibTeX XMLCite \textit{N. Bhardwaj} and \textit{C.-M. Tran}, J. Symb. Log. 86, No. 4, 1324--1349 (2021; Zbl 07457781) Full Text: DOI arXiv
Dimitrov, Stoyan Pairs of square-free values of the type \(n^2+1\), \(n^2+2\). (English) Zbl 07442468 Czech. Math. J. 71, No. 4, 991-1009 (2021). MSC: 11L05 11N25 11N37 PDFBibTeX XMLCite \textit{S. Dimitrov}, Czech. Math. J. 71, No. 4, 991--1009 (2021; Zbl 07442468) Full Text: DOI arXiv
Brown, Ron The natural density of some sets of square-free numbers. (English) Zbl 1484.11187 Integers 21, Paper A81, 9 p. (2021). Reviewer: Jonas Šiaulys (Vilnius) MSC: 11N25 PDFBibTeX XMLCite \textit{R. Brown}, Integers 21, Paper A81, 9 p. (2021; Zbl 1484.11187) Full Text: arXiv Link
Carmon, Dan; Entin, Alexei On square-free values of large polynomials over the rational function field. (English) Zbl 1480.11113 Math. Proc. Camb. Philos. Soc. 170, No. 2, 247-263 (2021). MSC: 11N25 11N32 11N36 11R58 14H05 PDFBibTeX XMLCite \textit{D. Carmon} and \textit{A. Entin}, Math. Proc. Camb. Philos. Soc. 170, No. 2, 247--263 (2021; Zbl 1480.11113) Full Text: DOI arXiv
Gorodetsky, Ofir; Matomäki, Kaisa; Radziwiłł, Maksym; Rodgers, Brad On the variance of squarefree integers in short intervals and arithmetic progressions. (English) Zbl 1473.11180 Geom. Funct. Anal. 31, No. 1, 111-149 (2021). Reviewer: D. R. Heath-Brown (Oxford) MSC: 11N25 11M26 11N37 PDFBibTeX XMLCite \textit{O. Gorodetsky} et al., Geom. Funct. Anal. 31, No. 1, 111--149 (2021; Zbl 1473.11180) Full Text: DOI arXiv
Kim, Jaeyoon; Volkovich, Ilya; Zhang, Nelson Xuzhi The power of Leibniz-like functions as oracles. (English) Zbl 07603927 Fernau, Henning, Computer science – theory and applications. 15th international computer science symposium in Russia, CSR 2020, Yekaterinburg, Russia, June 29 – July 3, 2020. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 12159, 263-275 (2020). MSC: 68Qxx PDFBibTeX XMLCite \textit{J. Kim} et al., Lect. Notes Comput. Sci. 12159, 263--275 (2020; Zbl 07603927) Full Text: DOI
Dimitrov, S. I. Consecutive square-free values of the form \([\alpha p]\), \([\alpha p]+1\). (English) Zbl 1489.11142 Proc. Jangjeon Math. Soc. 23, No. 4, 519-524 (2020). MSC: 11N25 11N37 11L20 11P32 PDFBibTeX XMLCite \textit{S. I. Dimitrov}, Proc. Jangjeon Math. Soc. 23, No. 4, 519--524 (2020; Zbl 1489.11142) Full Text: DOI arXiv
Munsch, Marc; Shparlinski, Igor E. On smooth square-free numbers in arithmetic progressions. (English) Zbl 1469.11375 J. Lond. Math. Soc., II. Ser. 101, No. 3, 1041-1067 (2020). Reviewer: Mehdi Hassani (Zanjan) MSC: 11N25 11B25 11L40 PDFBibTeX XMLCite \textit{M. Munsch} and \textit{I. E. Shparlinski}, J. Lond. Math. Soc., II. Ser. 101, No. 3, 1041--1067 (2020; Zbl 1469.11375) Full Text: DOI arXiv
Dimitrov, Stoyan On the number of pairs of positive integers \(x, y \leq H\) such that \(x^2+y^2+1, x^2+y^2+2\) are square-free. (English) Zbl 1469.11263 Acta Arith. 194, No. 3, 281-294 (2020). Reviewer: Alexey Ustinov (Khabarovsk) MSC: 11L05 11N25 11N37 PDFBibTeX XMLCite \textit{S. Dimitrov}, Acta Arith. 194, No. 3, 281--294 (2020; Zbl 1469.11263) Full Text: DOI arXiv
Dimitrov, S. I. On the distribution of consecutive square-free numbers of the form \([\alpha n], [\alpha n]+1\). (English) Zbl 1428.11163 Proc. Jangjeon Math. Soc. 22, No. 3, 463-470 (2019). MSC: 11N25 11L05 11N37 PDFBibTeX XMLCite \textit{S. I. Dimitrov}, Proc. Jangjeon Math. Soc. 22, No. 3, 463--470 (2019; Zbl 1428.11163) Full Text: arXiv
de la Bretèche, Régis; Tenenbaum, Gérald Gál-type sums and applications. (Sommes de Gál et applications.) (French. English summary) Zbl 1458.11141 Proc. Lond. Math. Soc. (3) 119, No. 1, 104-134 (2019). Reviewer: Jonas Šiaulys (Vilnius) MSC: 11N37 11A05 11L40 11M06 11N25 PDFBibTeX XMLCite \textit{R. de la Bretèche} and \textit{G. Tenenbaum}, Proc. Lond. Math. Soc. (3) 119, No. 1, 104--134 (2019; Zbl 1458.11141) Full Text: DOI arXiv
Dimitrov, S. I. Consecutive square-free numbers of the form \([n^c]\), \([n^c]+1\). (English) Zbl 1417.11145 JP J. Algebra Number Theory Appl. 40, No. 6, 945-956 (2018). MSC: 11N25 PDFBibTeX XMLCite \textit{S. I. Dimitrov}, JP J. Algebra Number Theory Appl. 40, No. 6, 945--956 (2018; Zbl 1417.11145) Full Text: DOI
Eggleton, Roger B.; Kimberley, Jason S.; MacDougall, James A. Square-free rank of integers. (English) Zbl 1439.11005 J. Comb. Math. Comb. Comput. 106, 185-207 (2018). MSC: 11A05 11B83 PDFBibTeX XMLCite \textit{R. B. Eggleton} et al., J. Comb. Math. Comb. Comput. 106, 185--207 (2018; Zbl 1439.11005)
Harnchoowong, Ajchara; Ponrod, Pitchayatak Unit groups of quotient rings of integers in some cubic fields. (English) Zbl 1409.11092 Commun. Korean Math. Soc. 32, No. 4, 789-803 (2017). MSC: 11R16 PDFBibTeX XMLCite \textit{A. Harnchoowong} and \textit{P. Ponrod}, Commun. Korean Math. Soc. 32, No. 4, 789--803 (2017; Zbl 1409.11092) Full Text: DOI
Dietmann, Rainer; Elsholtz, Christian; Shparlinski, Igor E. Prescribing the binary digits of squarefree numbers and quadratic residues. (English) Zbl 1431.11015 Trans. Am. Math. Soc. 369, No. 12, 8369-8388 (2017). MSC: 11A63 11B30 11N25 11H06 11L40 11P70 11T30 PDFBibTeX XMLCite \textit{R. Dietmann} et al., Trans. Am. Math. Soc. 369, No. 12, 8369--8388 (2017; Zbl 1431.11015) Full Text: DOI arXiv
Cohen, Stephen D.; Trudgian, Tim On the least square-free primitive root modulo \(p\). (English) Zbl 1402.11006 J. Number Theory 170, 10-16 (2017). MSC: 11A07 11L03 11A05 PDFBibTeX XMLCite \textit{S. D. Cohen} and \textit{T. Trudgian}, J. Number Theory 170, 10--16 (2017; Zbl 1402.11006) Full Text: DOI arXiv
Banerjee, Debika; Minamide, Makoto On an analogue of Buchstab’s identity. (English) Zbl 1376.11069 Notes Number Theory Discrete Math. 22, No. 1, 8-17 (2016). MSC: 11N25 11N37 PDFBibTeX XMLCite \textit{D. Banerjee} and \textit{M. Minamide}, Notes Number Theory Discrete Math. 22, No. 1, 8--17 (2016; Zbl 1376.11069) Full Text: Link
Shevelev, Vladimir \(S\)-exponential numbers. (English) Zbl 1402.11011 Acta Arith. 175, No. 4, 385-395 (2016). MSC: 11A51 11B05 PDFBibTeX XMLCite \textit{V. Shevelev}, Acta Arith. 175, No. 4, 385--395 (2016; Zbl 1402.11011) Full Text: DOI
Maier, Helmut; Rassias, Michael Th. Large gaps between consecutive prime numbers containing square-free numbers and perfect powers of prime numbers. (English) Zbl 1338.11085 Proc. Am. Math. Soc. 144, No. 8, 3347-3354 (2016). Reviewer: D. R. Heath-Brown (Oxford) MSC: 11N05 11N25 PDFBibTeX XMLCite \textit{H. Maier} and \textit{M. Th. Rassias}, Proc. Am. Math. Soc. 144, No. 8, 3347--3354 (2016; Zbl 1338.11085) Full Text: DOI arXiv
Aryan, Farzad Distribution of squares modulo a composite number. (English) Zbl 1372.11095 Int. Math. Res. Not. 2015, No. 23, 12405-12431 (2015). Reviewer: Jonas Šiaulys (Vilnius) MSC: 11N36 11N35 11N69 11L07 PDFBibTeX XMLCite \textit{F. Aryan}, Int. Math. Res. Not. 2015, No. 23, 12405--12431 (2015; Zbl 1372.11095) Full Text: DOI arXiv
Mauduit, Christian; Moreira, Carlos Gustavo Moser-Newman phenomenon for square-free numbers. (Phénomène de Moser-Newman pour les nombres sans facteur carré.) (French. English summary) Zbl 1352.11015 Bull. Soc. Math. Fr. 143, No. 3, 599-617 (2015). Reviewer: Wolfgang Steiner (Sydney) MSC: 11A63 11B85 11L03 11N25 PDFBibTeX XMLCite \textit{C. Mauduit} and \textit{C. G. Moreira}, Bull. Soc. Math. Fr. 143, No. 3, 599--617 (2015; Zbl 1352.11015) Full Text: DOI Link
Liu, Huaning; Dong, Hui On the distribution of square-free numbers. (Chinese. English summary) Zbl 1340.11078 J. Northwest Univ., Nat. Sci. Ed. 45, No. 1, 1-9 (2015). MSC: 11N25 11N36 PDFBibTeX XMLCite \textit{H. Liu} and \textit{H. Dong}, J. Northwest Univ., Nat. Sci. Ed. 45, No. 1, 1--9 (2015; Zbl 1340.11078) Full Text: DOI
Liu, Huaning; Dong, Hui On the distribution of consecutive square-free primitive roots modulo \(p\). (English) Zbl 1363.11090 Czech. Math. J. 65, No. 2, 555-564 (2015). MSC: 11N25 11B50 11L40 PDFBibTeX XMLCite \textit{H. Liu} and \textit{H. Dong}, Czech. Math. J. 65, No. 2, 555--564 (2015; Zbl 1363.11090) Full Text: DOI Link
Chen, Yong-Gao; Mei, Shu-Yuan Integers with a given number of divisors. (English) Zbl 1353.11014 J. Number Theory 143, 109-124 (2014). MSC: 11B05 11A25 11A41 PDFBibTeX XMLCite \textit{Y.-G. Chen} and \textit{S.-Y. Mei}, J. Number Theory 143, 109--124 (2014; Zbl 1353.11014) Full Text: DOI
Chung, Ping Ngai; Li, Shiyu Bounded gaps between products of special primes. (English) Zbl 1296.11118 Mathematics 2, No. 1, 37-52 (2014). MSC: 11N05 11N25 11G05 PDFBibTeX XMLCite \textit{P. N. Chung} and \textit{S. Li}, Mathematics 2, No. 1, 37--52 (2014; Zbl 1296.11118) Full Text: DOI
Shparlinski, Igor E. Squarefree parts of discriminants of trinomials. (English) Zbl 1316.11083 Arch. Math. 102, No. 6, 545-554 (2014). Reviewer: D. R. Heath-Brown (Oxford) MSC: 11N25 11N36 11L40 11C08 PDFBibTeX XMLCite \textit{I. E. Shparlinski}, Arch. Math. 102, No. 6, 545--554 (2014; Zbl 1316.11083) Full Text: DOI
Mei, Shu-Yuan A new class of ordinary integers. (English) Zbl 1295.11006 J. Number Theory 133, No. 10, 3559-3564 (2013). MSC: 11A25 11A41 PDFBibTeX XMLCite \textit{S.-Y. Mei}, J. Number Theory 133, No. 10, 3559--3564 (2013; Zbl 1295.11006) Full Text: DOI
Heath-Brown, D. R. Square-free values of \(n^2+1\). (English) Zbl 1312.11077 Acta Arith. 155, No. 1, 1-13 (2012). Reviewer: Angel V. Kumchev (Towson) MSC: 11N32 11D45 PDFBibTeX XMLCite \textit{D. R. Heath-Brown}, Acta Arith. 155, No. 1, 1--13 (2012; Zbl 1312.11077) Full Text: DOI arXiv
Kanemitsu, Shigeru; Laurinčikas, Antanas; Ma, Jing Square-free integers as ideal norms. (English) Zbl 1234.11130 Acta Math. Sin., Engl. Ser. 26, No. 4, 621-628 (2010). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11N37 11M41 11N25 11R11 11R29 11R42 PDFBibTeX XMLCite \textit{S. Kanemitsu} et al., Acta Math. Sin., Engl. Ser. 26, No. 4, 621--628 (2010; Zbl 1234.11130) Full Text: DOI
Ichimura, Humio Note on Galois descent of a normal integral basis of acyclic extension of degree \(p\). (English) Zbl 1232.11119 Proc. Japan Acad., Ser. A 85, No. 10, 160-162 (2009). Reviewer: Günter Lettl (Graz) MSC: 11R33 PDFBibTeX XMLCite \textit{H. Ichimura}, Proc. Japan Acad., Ser. A 85, No. 10, 160--162 (2009; Zbl 1232.11119) Full Text: DOI
Kaczorowski, Jerzy; Wiertelak, Kazimierz Oscillations of a given size of some arithmetic error terms. (English) Zbl 1184.11029 Trans. Am. Math. Soc. 361, No. 9, 5023-5039 (2009). Reviewer: Ekkehard Krätzel (Wien) MSC: 11N05 11N13 11N25 11M26 PDFBibTeX XMLCite \textit{J. Kaczorowski} and \textit{K. Wiertelak}, Trans. Am. Math. Soc. 361, No. 9, 5023--5039 (2009; Zbl 1184.11029) Full Text: DOI
Shi, Sanying Mean value of the error term for the number of square-free numbers. (English) Zbl 1184.11030 JP J. Algebra Number Theory Appl. 13, No. 1, 27-34 (2009). Reviewer: Ekkehard Krätzel (Wien) MSC: 11N25 PDFBibTeX XMLCite \textit{S. Shi}, JP J. Algebra Number Theory Appl. 13, No. 1, 27--34 (2009; Zbl 1184.11030) Full Text: Link
Kurlberg, Pär Poisson spacing statistics for value sets of polynomials. (English) Zbl 1231.11118 Int. J. Number Theory 5, No. 3, 489-513 (2009). Reviewer: Jonas Šiaulys (Vilnius) MSC: 11N69 11K36 12E10 PDFBibTeX XMLCite \textit{P. Kurlberg}, Int. J. Number Theory 5, No. 3, 489--513 (2009; Zbl 1231.11118) Full Text: DOI arXiv
Banks, William D.; Luca, Florian; Szalay, László A variant on the notion of a Diophantine \(s\)-tuple. (English) Zbl 1219.11044 Glasg. Math. J. 51, No. 1, 83-89 (2009). Reviewer: Andrej Dujella (Zagreb) MSC: 11B99 11D99 11N25 PDFBibTeX XMLCite \textit{W. D. Banks} et al., Glasg. Math. J. 51, No. 1, 83--89 (2009; Zbl 1219.11044) Full Text: DOI
Sun, Xuegong; Liu, Wei Representing integers by a sum of two coprime square-free numbers. (English) Zbl 1199.11115 J. Nanjing Norm. Univ., Nat. Sci. Ed. 31, No. 4, 37-39 (2008). MSC: 11N25 11D04 PDFBibTeX XMLCite \textit{X. Sun} and \textit{W. Liu}, J. Nanjing Norm. Univ., Nat. Sci. Ed. 31, No. 4, 37--39 (2008; Zbl 1199.11115)
Cao, Xiaodong; Zhai, Wenguang On the distribution of square-free numbers of the form \([n^c]\). II. (Chinese. English summary) Zbl 1174.11395 Acta Math. Sin., Chin. Ser. 51, No. 6, 1187-1194 (2008). MSC: 11N25 11L07 PDFBibTeX XMLCite \textit{X. Cao} and \textit{W. Zhai}, Acta Math. Sin., Chin. Ser. 51, No. 6, 1187--1194 (2008; Zbl 1174.11395)
Guo, Ruting Mean value estimate for the greatest divisors of \(N\) which is prime to a certain integer. II. (Chinese. English summary) Zbl 1174.11397 J. Shandong Univ., Nat. Sci. 43, No. 6, 34-36, 43 (2008). MSC: 11N25 PDFBibTeX XMLCite \textit{R. Guo}, J. Shandong Univ., Nat. Sci. 43, No. 6, 34--36, 43 (2008; Zbl 1174.11397)
Alkan, Emre; Ledoan, Andrew H.; Vâjâitu, Marian; Zaharescu, Alexandru On the index of fractions with square-free denominators in arithmetic progressions. (English) Zbl 1182.11012 Ramanujan J. 16, No. 2, 131-161 (2008). Reviewer: Stephan Baier (Bristol) MSC: 11B57 11M06 11N25 PDFBibTeX XMLCite \textit{E. Alkan} et al., Ramanujan J. 16, No. 2, 131--161 (2008; Zbl 1182.11012) Full Text: DOI
Guo, Ruting Mean value estimate for the greatest divisors of a number which is prime to a certain integer. (Chinese. English summary) Zbl 1174.11396 J. Shandong Univ., Nat. Sci. 42, No. 11, 110-113 (2007). MSC: 11N25 PDFBibTeX XMLCite \textit{R. Guo}, J. Shandong Univ., Nat. Sci. 42, No. 11, 110--113 (2007; Zbl 1174.11396)
Shevelev, Vladimir Compact integers and factorials. (English) Zbl 1112.11006 Acta Arith. 126, No. 3, 195-236 (2007). Reviewer: Tom M. Apostol (Pasadena) MSC: 11A51 11B65 11D61 11N05 PDFBibTeX XMLCite \textit{V. Shevelev}, Acta Arith. 126, No. 3, 195--236 (2007; Zbl 1112.11006) Full Text: DOI
Zhai, Wenguang; Liu, Huaning On square-free primitive roots mod \(p\). (English) Zbl 1184.11031 Sci. Magna 2, No. 2, 15-19 (2006). MSC: 11N25 PDFBibTeX XMLCite \textit{W. Zhai} and \textit{H. Liu}, Sci. Magna 2, No. 2, 15--19 (2006; Zbl 1184.11031)
Tolev, D. I. On the distribution of \(r\)-tuples of squarefree numbers in short intervals. (English) Zbl 1196.11130 Int. J. Number Theory 2, No. 2, 225-234 (2006). Reviewer: Roger Heath-Brown (Oxford) MSC: 11N25 11N36 11N37 PDFBibTeX XMLCite \textit{D. I. Tolev}, Int. J. Number Theory 2, No. 2, 225--234 (2006; Zbl 1196.11130) Full Text: DOI arXiv
Kátai, Imre Square-free values of the Carmichael function. (English) Zbl 1119.11055 Math. Pannonica 16, No. 2, 199-203 (2005). Reviewer: Ferenc Mátyás (Eger) MSC: 11N25 11N36 PDFBibTeX XMLCite \textit{I. Kátai}, Math. Pannonica 16, No. 2, 199--203 (2005; Zbl 1119.11055) Full Text: EuDML
Schlage-Puchta, Jan-Christoph The exponential sum over squarefree integers. (English) Zbl 1059.11048 Acta Arith. 115, No. 3, 265-268 (2004). Reviewer: Roger Heath-Brown (Oxford) MSC: 11L07 11N25 11P55 PDFBibTeX XMLCite \textit{J.-C. Schlage-Puchta}, Acta Arith. 115, No. 3, 265--268 (2004; Zbl 1059.11048) Full Text: DOI arXiv
Pappalardi, Francesco Square free values of the order function. (English) Zbl 1066.11044 New York J. Math. 9, 331-344 (2003). MSC: 11N37 11N56 PDFBibTeX XMLCite \textit{F. Pappalardi}, New York J. Math. 9, 331--344 (2003; Zbl 1066.11044) Full Text: EuDML EMIS
Dubickas, A. Asymptotic density of surds with stable height. (English) Zbl 1145.11330 Acta Appl. Math. 78, No. 1-3, 99-102 (2003). MSC: 11R04 PDFBibTeX XMLCite \textit{A. Dubickas}, Acta Appl. Math. 78, No. 1--3, 99--102 (2003; Zbl 1145.11330) Full Text: DOI
Pappalardi, Francesco; Saidak, Filip; Shparlinski, Igor E. Square-free values of the Carmichael function. (English) Zbl 1042.11058 J. Number Theory 103, No. 1, 122-131 (2003). Reviewer: Florian Luca (Morelia) MSC: 11N25 11N05 11N37 PDFBibTeX XMLCite \textit{F. Pappalardi} et al., J. Number Theory 103, No. 1, 122--131 (2003; Zbl 1042.11058) Full Text: DOI
Nicolas, J.-L. Statistical properties of partitions. (English) Zbl 1050.11088 Halász, Gábor (ed.) et al., Paul Erdős and his mathematics I. Based on the conference, Budapest, Hungary, July 4–11, 1999. Berlin: Springer; Budapest: János Bolyai Mathematical Society (ISBN 3-540-42236-6/2-vol.-set; 963-8022-96-5). Bolyai Soc. Math. Stud. 11, 537-547 (2002). Reviewer: Ljuben Mutafchiev (Tampa) MSC: 11P82 05A17 11N36 01A70 01A60 11-03 PDFBibTeX XMLCite \textit{J. L. Nicolas}, Bolyai Soc. Math. Stud. 11, 537--547 (2002; Zbl 1050.11088)
Gyarmati, Katalin On divisibility properties of integers of the form \(ab+1\). (English) Zbl 0980.11039 Period. Math. Hung. 43, No. 1-2, 71-79 (2001). Reviewer: Christian Elsholtz (Clausthal-Zellerfeld) MSC: 11N25 11N36 05C35 PDFBibTeX XMLCite \textit{K. Gyarmati}, Period. Math. Hung. 43, No. 1--2, 71--79 (2001; Zbl 0980.11039) Full Text: DOI
Panaitopol, Laurenţiu On square free integers. (English) Zbl 1053.11077 Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 43(91), No. 1, 19-23 (2000). Reviewer: Toma Albu (Bucureşti) MSC: 11N05 11A25 PDFBibTeX XMLCite \textit{L. Panaitopol}, Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 43(91), No. 1, 19--23 (2000; Zbl 1053.11077)
Cao, Xiaodong; Zhai, Wenguang The distribution of square-free numbers of the form \([n^c]\). (English) Zbl 0926.11066 J. Théor. Nombres Bordx. 10, No. 2, 287-299 (1998). Reviewer: E.Krätzel (Wien) MSC: 11N25 11L07 PDFBibTeX XMLCite \textit{X. Cao} and \textit{W. Zhai}, J. Théor. Nombres Bordx. 10, No. 2, 287--299 (1998; Zbl 0926.11066) Full Text: DOI Numdam EuDML EMIS
Brüdern, J.; Granville, A.; Perelli, A.; Vaughan, R. C.; Wooley, T. D. On the exponential sum over \(k\)-free numbers. (English) Zbl 0922.11071 Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 356, No. 1738, 739-761 (1998). Reviewer: D.Goldston (San Jose) MSC: 11L07 11N25 11P55 11P05 PDFBibTeX XMLCite \textit{J. Brüdern} et al., Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 356, No. 1738, 739--761 (1998; Zbl 0922.11071) Full Text: DOI
Huxley, M. N. Moments of differences between square-free numbers. (English) Zbl 0932.11057 Greaves, G. R. H. (ed.) et al., Sieve methods, exponential sums, and their applications in number theory. Proceedings of a symposium, Cardiff, UK, July 17–21, 1995. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 237, 187-204 (1997). Reviewer: G.Kolesnik (Los Angeles) MSC: 11N25 PDFBibTeX XMLCite \textit{M. N. Huxley}, Lond. Math. Soc. Lect. Note Ser. 237, 187--204 (1997; Zbl 0932.11057)
Sankaranayanan, A. On the sign changes in the remainder term of an asymptotic formula for the number of square-free numbers. (English) Zbl 0809.11048 Arch. Math. 60, No. 1, 51-57 (1993). Reviewer: J.Kaczorowski (Poznań) MSC: 11N25 PDFBibTeX XMLCite \textit{A. Sankaranayanan}, Arch. Math. 60, No. 1, 51--57 (1993; Zbl 0809.11048) Full Text: DOI
Jia, Chaohua The distribution of square-free numbers. (English) Zbl 0772.11033 Sci. China, Ser. A 36, No. 2, 154-169 (1993). Reviewer: P.Shiu (Loughborough) MSC: 11N25 11L07 PDFBibTeX XMLCite \textit{C. Jia}, Sci. China, Ser. A 36, No. 2, 154--169 (1993; Zbl 0772.11033)
Laubenbacher, Reinhard C.; Magurn, Bruce A. \(SK_ 2\) and \(K_ 3\) of dihedral groups. (English) Zbl 0780.19004 Can. J. Math. 44, No. 3, 591-623 (1992). MSC: 19C40 19D50 PDFBibTeX XMLCite \textit{R. C. Laubenbacher} and \textit{B. A. Magurn}, Can. J. Math. 44, No. 3, 591--623 (1992; Zbl 0780.19004) Full Text: DOI
Yu, Hongbing; Wang, Qiaoling On the representations of a number as the sum of two square-free numbers. (Chinese. English summary) Zbl 0774.11057 J. China Univ. Sci. Technol. 22, No. 4, 440-444 (1992). Reviewer: Xuan Tizuo (Beijing) MSC: 11N37 11N25 PDFBibTeX XMLCite \textit{H. Yu} and \textit{Q. Wang}, J. China Univ. Sci. Technol. 22, No. 4, 440--444 (1992; Zbl 0774.11057)
Bartz, Krystyna Maria On some connections between zeta-zeros and square-free integers. (English) Zbl 0764.11039 Monatsh. Math. 114, No. 1, 15-34 (1992). Reviewer: K.M.Bartz (Poznán) MSC: 11N25 11M26 PDFBibTeX XMLCite \textit{K. M. Bartz}, Monatsh. Math. 114, No. 1, 15--34 (1992; Zbl 0764.11039) Full Text: DOI EuDML
Langevin, Michel Partie sans facteur carré d’un produit d’entiers voisins. (Square-free divisor of a product of neighbouring integers). (French) Zbl 0776.11058 Approximations diophantiennes et nombres transcendants, C.-R. Colloq., Luminy/ Fr. 1990, 203-214 (1992). Reviewer: P.Vojta (Berkeley) MSC: 11N25 11J86 PDFBibTeX XMLCite \textit{M. Langevin}, in: Approximations diophantiennes et nombres transcendants. Comptes-rendus du colloque tenu au C.I.R.M. de Luminy, France, 18-22 Juin, 1990. Berlin etc.: de Gruyter. 203--214 (1992; Zbl 0776.11058)
Grimmett, G. R.; Hall, R. R. The asymptotics of random sieves. (English) Zbl 0725.11044 Mathematika 38, No. 2, 285-302 (1991). Reviewer: G. R. Grimmett (Bristol) MSC: 11N35 11N25 11N36 PDFBibTeX XMLCite \textit{G. R. Grimmett} and \textit{R. R. Hall}, Mathematika 38, No. 2, 285--302 (1991; Zbl 0725.11044) Full Text: DOI
Baker, R. C.; Brüdern, J. Sums of cubes of square-free numbers. (English) Zbl 0718.11046 Monatsh. Math. 111, No. 1, 1-21 (1991). Reviewer: R.C.Baker MSC: 11P05 11L07 11P55 PDFBibTeX XMLCite \textit{R. C. Baker} and \textit{J. Brüdern}, Monatsh. Math. 111, No. 1, 1--21 (1991; Zbl 0718.11046) Full Text: DOI EuDML
Baker, R. C.; Brüdern, J. Sums of cubes of square-free numbers. II. (English) Zbl 0736.11056 Monatsh. Math. 112, No. 3, 177-207 (1991). Reviewer: J.Brüdern (Göttingen) MSC: 11P05 11L07 11P55 PDFBibTeX XMLCite \textit{R. C. Baker} and \textit{J. Brüdern}, Monatsh. Math. 112, No. 3, 177--207 (1991; Zbl 0736.11056) Full Text: DOI EuDML
Spiro, Claudia A. The probability that the number of groups of squarefree order is two more than a fixed prime. (English) Zbl 0707.11066 Proc. Lond. Math. Soc., III. Ser. 60, No. 3, 444-470 (1990). Reviewer: Ekkehard Krätzel (Jena) MSC: 11N45 PDFBibTeX XMLCite \textit{C. A. Spiro}, Proc. Lond. Math. Soc. (3) 60, No. 3, 444--470 (1990; Zbl 0707.11066) Full Text: DOI
Györy, K.; Mignotte, M.; Shorey, T. N. On some arithmetical properties of weighted sums of S-units. (English) Zbl 0738.11034 Math. Pannonica 1, No. 2, 25-43 (1990). Reviewer: J.-H.Evertse (Leiden) MSC: 11D57 11D85 11D61 11D72 11J86 PDFBibTeX XMLCite \textit{K. Györy} et al., Math. Pannonica 1, No. 2, 25--43 (1990; Zbl 0738.11034) Full Text: EuDML
Qiu, Zhuoming; Zhao, E. On a problem of Suryanarayana. II. (Chinese. English summary) Zbl 0705.11054 J. Shandong Univ., Nat. Sci. Ed. 24, No. 3, 20-26 (1989). Reviewer: P.Shiu MSC: 11N37 11N25 PDFBibTeX XMLCite \textit{Z. Qiu} and \textit{E. Zhao}, J. Shandong Univ., Nat. Sci. Ed. 24, No. 3, 20--26 (1989; Zbl 0705.11054)
Popov, O. V. Quadratic residues and nonresidues in a square-free numbers sequence. (English. Russian original) Zbl 0697.10038 Mosc. Univ. Math. Bull. 44, No. 5, 77-79 (1989); translation from Vestn. Mosk. Univ., Ser. I 1989, No. 5, 81-83 (1989). MSC: 11N69 11L40 11A15 PDFBibTeX XMLCite \textit{O. V. Popov}, Mosc. Univ. Math. Bull. 44, No. 5, 77--79 (1989; Zbl 0697.10038); translation from Vestn. Mosk. Univ., Ser. I 1989, No. 5, 81--83 (1989)
Hinz, Jürgen G. Square-free values of cubic polynomials in algebraic number fields. (English) Zbl 0686.12001 J. Number Theory 32, No. 3, 307-320 (1989). Reviewer: M.Nair MSC: 11R09 11R04 PDFBibTeX XMLCite \textit{J. G. Hinz}, J. Number Theory 32, No. 3, 307--320 (1989; Zbl 0686.12001) Full Text: DOI
Popov, O. V. On quadratic residues and nonresidues in the sequence of square-free numbers. (Russian) Zbl 0684.10046 Vestn. Mosk. Univ., Ser. I 1989, No. 5, 81-83 (1989). Reviewer: W.Narkiewicz MSC: 11N69 11L40 11A15 PDFBibTeX XMLCite \textit{O. V. Popov}, Vestn. Mosk. Univ., Ser. I 1989, No. 5, 81--83 (1989; Zbl 0684.10046)
Harman, Glyn Metric diophantine approximation with two restricted variables. I: Two square-free integers, or integers in arithmetic progressions. (English) Zbl 0655.10047 Math. Proc. Camb. Philos. Soc. 103, No. 2, 197-206 (1988). Reviewer: M.-C.Liu MSC: 11K60 11J70 11J04 PDFBibTeX XMLCite \textit{G. Harman}, Math. Proc. Camb. Philos. Soc. 103, No. 2, 197--206 (1988; Zbl 0655.10047) Full Text: DOI
Györy, K.; Shorey, T. N. On the denominators of equivalent algebraic numbers. (English) Zbl 0643.12001 Indag. Math. 50, No. 1, 29-41 (1988). Reviewer: J.Silverman MSC: 11R04 11D41 PDFBibTeX XMLCite \textit{K. Györy} and \textit{T. N. Shorey}, Indag. Math. 50, No. 1, 29--41 (1988; Zbl 0643.12001)
Baker, R. C. Square-free points on ellipsoids. (English) Zbl 0591.10014 Acta Arith. 50, No. 3, 215-219 (1988). MSC: 11E16 11D85 PDFBibTeX XMLCite \textit{R. C. Baker}, Acta Arith. 50, No. 3, 215--219 (1988; Zbl 0591.10014) Full Text: DOI EuDML
Tutushev, Sh. Kh. Some applications of the method of complex integration in problems of number theory. (Russian) Zbl 0631.10027 Izv. Sev.-Kavk. Nauchn. Tsentra Vyssh. Shk., Estestv. Nauki 1987, No. 1(57), 20-21 (1987). Reviewer: G. A. Kolesnik (Los Angeles) MSC: 11N37 11N05 PDFBibTeX XMLCite \textit{Sh. Kh. Tutushev}, Izv. Sev.-Kavk. Nauchn. Tsentra Vyssh. Shk., Estestv. Nauki 1987, No. 1(57), 20--21 (1987; Zbl 0631.10027)
Lyashenko, N. N. Arithmetic modeling of the Wiener process, and the Möbius function. (English. Russian original) Zbl 0626.60075 Sov. Math., Dokl. 34, 345-348 (1987); translation from Dokl. Akad. Nauk SSSR 290, 786-788 (1986). Reviewer: Murali Rao MSC: 60J65 11K65 11L40 PDFBibTeX XMLCite \textit{N. N. Lyashenko}, Sov. Math., Dokl. 34, 345--348 (1987; Zbl 0626.60075); translation from Dokl. Akad. Nauk SSSR 290, 786--788 (1986)
Erdős, Paul; Sárközy, A. On divisibility properties of integers of the form \(a+a'\). (English) Zbl 0625.10038 Acta Math. Hung. 50, 117-122 (1987). Reviewer: K.Ramachandra MSC: 11N35 11B83 PDFBibTeX XMLCite \textit{P. Erdős} and \textit{A. Sárközy}, Acta Math. Hung. 50, 117--122 (1987; Zbl 0625.10038) Full Text: DOI
De Koninck, Jean-Marie; Sitaramachandrarao, R. Sums involving the largest prime divisor of an integer. (English) Zbl 0578.10046 Acta Arith. 48, 1-8 (1987). MSC: 11N37 PDFBibTeX XMLCite \textit{J.-M. De Koninck} and \textit{R. Sitaramachandrarao}, Acta Arith. 48, 1--8 (1987; Zbl 0578.10046) Full Text: DOI EuDML
Vil’chinskij, V. T. On diophantine approximations with square-free numbers. (Russian. English summary) Zbl 0607.10035 Izv. Akad. Nauk BSSR, Ser. Fiz.-Mat. Nauk 1986, No. 3, 9-13 (1986). MSC: 11K60 11J83 PDFBibTeX XMLCite \textit{V. T. Vil'chinskij}, Izv. Akad. Nauk BSSR, Ser. Fiz.-Mat. Nauk 1986, No. 3, 9--13 (1986; Zbl 0607.10035)
Erdős, Paul Some problems on number theory. (English) Zbl 0584.10002 Publ. Math. Orsay 86/01, 53-67 (1986). Reviewer: Eira J. Scourfield (Egham) MSC: 11-02 11N05 00A27 PDFBibTeX XMLCite \textit{P. Erdős}, Publ. Math. Orsay 86/01, 53--67 (1986; Zbl 0584.10002)
Tsang, Kai-Man The distribution of \(r\)-tuples of square-free numbers. (English) Zbl 0583.10026 Mathematika 32, 265-275 (1985). Reviewer: P.Shiu MSC: 11N05 11N35 PDFBibTeX XMLCite \textit{K.-M. Tsang}, Mathematika 32, 265--275 (1985; Zbl 0583.10026) Full Text: DOI
Heath-Brown, D. R. Diophantine approximation with square-free numbers. (English) Zbl 0539.10026 Math. Z. 187, 335-344 (1984). MSC: 11J04 11H06 11N35 PDFBibTeX XMLCite \textit{D. R. Heath-Brown}, Math. Z. 187, 335--344 (1984; Zbl 0539.10026) Full Text: DOI EuDML
Harman, Glyn Diophantine approximation with square-free integers. (English) Zbl 0539.10025 Math. Proc. Camb. Philos. Soc. 95, 381-388 (1984). Reviewer: D.R.Heath-Brown MSC: 11J04 11K60 PDFBibTeX XMLCite \textit{G. Harman}, Math. Proc. Camb. Philos. Soc. 95, 381--388 (1984; Zbl 0539.10025) Full Text: DOI
Heath-Brown, D. R. The square sieve and consecutive square-free numbers. (English) Zbl 0514.10038 Math. Ann. 266, 251-259 (1984). MSC: 11N35 11N05 PDFBibTeX XMLCite \textit{D. R. Heath-Brown}, Math. Ann. 266, 251--259 (1984; Zbl 0514.10038) Full Text: DOI EuDML
Halberstam, Heini Gaps in integer sequences. (English) Zbl 0511.10001 Math. Mag. 56, 131-140 (1983). MSC: 11-01 11A41 11P05 11A05 11P21 PDFBibTeX XMLCite \textit{H. Halberstam}, Math. Mag. 56, 131--140 (1983; Zbl 0511.10001) Full Text: DOI
Lenstra, A. K. Factorization of polynomials. (English) Zbl 0509.12002 Computational methods in number theory, Part I, Math. Cent. Tracts 154, 169-198 (1982). MSC: 11R09 11T06 12-02 12-04 65H05 68Q25 11C08 PDFBibTeX XML
Sitaramaiah, V.; Suryanarayana, D. On certain divisor sums over square-full integers. (English) Zbl 0499.10048 Proc. Conf. Number Theory, Mysore 1979, Matsci. Rep. 101, 98-109 (1980). MSC: 11N37 PDFBibTeX XML
Subramanyam, P.; Suryanarayana, D. The maximal k-full divisor of an integer. (English) Zbl 0494.10032 Proc. Conf. Number Theory, Mysore 1979, Matsci. Rep. 101, 131-156 (1980). MSC: 11N05 11N37 PDFBibTeX XML
Greger, Karl Square divisors and square-free numbers. (English) Zbl 0391.10001 Math. Mag. 51, 211-219 (1978). Reviewer: Olaf Ninnemann (Uffing am Staffelsee) MSC: 11-01 11N25 PDFBibTeX XMLCite \textit{K. Greger}, Math. Mag. 51, 211--219 (1978; Zbl 0391.10001) Full Text: DOI
Bombieri, Enrico The asymptotic sieve. (English) Zbl 0422.10042 Rend., Accad. Naz. XL, V. Ser. 1-2, 243-269 (1976). MSC: 11N35 11N13 11N05 PDFBibTeX XML
Vaidya, A. M. On the order of the error function of the square-free numbers. (English) Zbl 0158.29701 Proc. Natl. Inst. Sci. India, Part A 32, 196-201 (1966). Reviewer: J. H. van Lint MSC: 11N25 PDFBibTeX XMLCite \textit{A. M. Vaidya}, Proc. Natl. Inst. Sci. India, Part A 32, 196--201 (1966; Zbl 0158.29701)