Chailangka, Natdanai; Pakapongpun, Apisit On a certain sequence of sequence \(t\)-Neo balancing numbers. (English) Zbl 07907958 Int. J. Math. Comput. Sci. 20, No. 1, 45-48 (2025). MSC: 11B37 11D25 × Cite Format Result Cite Review PDF Full Text: DOI
Singh, P. K.; Ray, S. Saha A numerical approach based on Pell polynomial for solving stochastic fractional differential equations. (English) Zbl 07958570 Numer. Algorithms 97, No. 4, 1513-1534 (2024). MSC: 60H35 60H10 65C30 × Cite Format Result Cite Review PDF Full Text: DOI
Azin, H.; Baghani, O.; Habibirad, A. The hyperbolic multi-term time fractional integro-differential equation with generalized Caputo derivative and error estimate in \(L_{p,\gamma,\upsilon}\) space. (English) Zbl 07955188 Z. Angew. Math. Phys. 75, No. 6, Paper No. 230, 24 p. (2024). MSC: 34K37 45K05 34M46 × Cite Format Result Cite Review PDF Full Text: DOI
Reinhart, Andreas A counterexample to the Pellian equation conjecture of Mordell. (English) Zbl 07914795 Acta Arith. 215, No. 1, 85-95 (2024). MSC: 11R11 11R27 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Fedorov, G. V. On the sequences of polynomials \(\boldsymbol{f}\) with a periodic continued fraction expansion \(\sqrt{\boldsymbol{f}} \). (English. Russian original) Zbl 07908863 Mosc. Univ. Math. Bull. 79, No. 2, 98-102 (2024); translation from Vestn. Mosk. Univ., Ser. I 79, No. 2, 25-30 (2024). Reviewer: Isabelle Dubois (Metz) MSC: 11J70 11R58 11R27 × Cite Format Result Cite Review PDF Full Text: DOI
Zannier, Umberto [Amoroso, Francesco] Lecture notes on Diophantine analysis. With an appendix by Francesco Amoroso. 2nd edition. (English) Zbl 07903163 EMS Series of Lectures in Mathematics 36. Berlin: European Mathematical Society (EMS) (ISBN 978-3-98547-077-8/pbk; 978-3-98547-577-3/ebook). xii, 399 p. (2024). Reviewer: István Gaál (Debrecen) MSC: 11-01 11D04 11D09 11D45 11D59 11G50 × Cite Format Result Cite Review PDF Full Text: DOI
Somanath, Manju; V. A., Bindu; Das, Radhika Solutions in integers for the quadratic Diophantine equation. (English) Zbl 07892905 Gaṇita 74, No. 1, 251-258 (2024). × Cite Format Result Cite Review PDF Full Text: Link
Ameur, Zahra; Boumahdi, Rachid; Garici, Tarek Some results concerning the exponential Diophantine equation \((a^n-1)(b^m-1) = x^2\). (English) Zbl 07881005 Indian J. Pure Appl. Math. 55, No. 2, 613-622 (2024). MSC: 11D41 11D61 × Cite Format Result Cite Review PDF Full Text: DOI
Kim, Seon-Hong; Stolarsky, Kenneth B. Translations and extensions of the Nicomachean identity. (English) Zbl 1543.11026 J. Integer Seq. 27, No. 6, Article 24.6.3, 23 p. (2024). Reviewer: Takao Komatsu (Hangzhou) MSC: 11B83 11D25 30C15 × Cite Format Result Cite Review PDF Full Text: Link
Ddamulira, Mahadi; Luca, Florian On the \(x\)-coordinates of Pell equations that are products of two Pell numbers. (English) Zbl 1547.11042 Math. Slovaca 74, No. 1, 41-56 (2024). Reviewer: Ingrid Vukusic (Waterloo) MSC: 11D09 11B39 11J86 × Cite Format Result Cite Review PDF Full Text: DOI
Alvanos, Paraskevas; Poulakis, Dimitrios Bounds for the smallest integral solution of Pell equation over a number field. (English) Zbl 1547.11041 Funct. Approximatio, Comment. Math. 70, No. 1, 41-54 (2024). Reviewer: Mahadi Ddamulira (Kampala) MSC: 11D09 12E12 11R80 × Cite Format Result Cite Review PDF Full Text: DOI
Gómez, Carlos A.; Rihane, Salah Eddine; Togbé, Alain On the \(X\)-coordinates of Pell equations \(X^2 - dY^2 = \pm 1\) as difference of two Fibonacci numbers. (English) Zbl 1540.11012 Int. J. Number Theory 20, No. 2, 487-506 (2024). Reviewer: Mahadi Ddamulira (Kampala) MSC: 11B39 11D09 11J86 × Cite Format Result Cite Review PDF Full Text: DOI
Scherr, Zachary; Thompson, Katherine Quartic integral polynomial Pell equations. (English) Zbl 1540.11020 J. Number Theory 259, 38-56 (2024). Reviewer: Nikos Tzanakis (Iraklion) MSC: 11C08 11D99 11G05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Walsh, P. G. Squares in recurrences using elliptic curves. (English) Zbl 1543.11052 Int. J. Number Theory 20, No. 1, 221-228 (2024). Reviewer: Maciej Ulas (Kraków) MSC: 11G05 11D09 × Cite Format Result Cite Review PDF Full Text: DOI
Walsh, P. G. Specializations of a generic rank-2 curve of Shioda. (English) Zbl 1540.11064 J. Number Theory 255, 1-7 (2024). Reviewer: Mentzelos Melistas (Enschede) MSC: 11G05 11D09 × Cite Format Result Cite Review PDF Full Text: DOI
Bruno, Giacomo; Corte-Real Santos, Maria; Costello, Craig; Eriksen, Jonathan Komada; Meyer, Michael; Naehrig, Michael; Sterner, Bruno Cryptographic smooth neighbors. (English) Zbl 1546.94057 Guo, Jian (ed.) et al., Advances in cryptology – ASIACRYPT 2023. 29th international conference on the theory and application of cryptology and information security, Guangzhou, China, December 4–8, 2023. Proceedings. Part VII. Singapore: Springer. Lect. Notes Comput. Sci. 14444, 190-221 (2023). MSC: 94A60 94A62 81P94 × Cite Format Result Cite Review PDF Full Text: DOI
Spier, Thomás Jung On means of near continued fractions. (English) Zbl 07856122 Integers 23, Paper A96, 11 p. (2023). Reviewer: Mykhaylo Pahirya (Uzhhorod) MSC: 11A55 11J70 11Y65 × Cite Format Result Cite Review PDF Full Text: arXiv Link
Guan, Xun Gui On simultaneous Pell equations \(x^2-(m^2-1) y^2=z^2-(n^2-1) y^2=1\). (Chinese. English summary) Zbl 07828134 Acta Math. Sin., Chin. Ser. 66, No. 1, 133-142 (2023). MSC: 11D09 11J86 × Cite Format Result Cite Review PDF Full Text: DOI
Das, Radhika; Somanath, Manju; Bindu, V. A. Integer solution analysis for a Diophantine equation with exponentials. (English) Zbl 1538.11088 Jñānābha 53, No. 2, 69-73 (2023). MSC: 11D09 × Cite Format Result Cite Review PDF Full Text: DOI
Somanath, Manju; Bindu, V. A.; Das, Radhika Solutions of Pell’s equation involving Sophie Germain primes. (English) Zbl 1538.11092 Jñānābha 53, No. 2, 40-43 (2023). MSC: 11D09 × Cite Format Result Cite Review PDF Full Text: DOI
Lee, Kwangwoo Automorphisms of \(\mathrm{K}3\) surfaces with Picard number two. (English) Zbl 1537.14056 Bull. Korean Math. Soc. 60, No. 6, 1427-1437 (2023). MSC: 14J28 14J50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Emin, Ahmet Some multi figurate numbers in terms of generalized Fibonacci and Lucas numbers. (English) Zbl 1538.11042 Aligarh Bull. Math. 42, No. 1, 107-123 (2023). MSC: 11B39 11D09 × Cite Format Result Cite Review PDF Full Text: Link
Çağman, Abdullah Repdigits as sums of three half-companion Pell numbers. (English) Zbl 1538.11033 Miskolc Math. Notes 24, No. 2, 687-697 (2023). MSC: 11B39 11D45 11J86 × Cite Format Result Cite Review PDF Full Text: DOI
Edjeou, Bilizimbéyé; Faye, Bernadette Pell and Pell-Lucas numbers as difference of two repdigits. (English) Zbl 1538.11041 Afr. Mat. 34, No. 4, Paper No. 70, 13 p. (2023). MSC: 11B39 11D61 11D45 11J86 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Goldfeld, Dorian; Hinkle, Gerhardt The cubic Pell equation \(L\)-function. (English) Zbl 1546.11135 Acta Arith. 210, 235-277 (2023). Reviewer: Sami Omar (Sukhair) MSC: 11M41 11F30 11D25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Lee, Kwangwoo The infinite dihedral group and \(K3\) surfaces with Picard number 2. (English) Zbl 1539.14073 Int. J. Math. 34, No. 12, Article ID 2350074, 15 p. (2023). Reviewer: Martina Monti (Milano) MSC: 14J28 14J50 × Cite Format Result Cite Review PDF Full Text: DOI
Walsh, P. G. A note on lower bounds for ranks using Pell equations. (English) Zbl 1524.11123 Rad Hrvat. Akad. Znan. Umjet. 555, Mat. Znan. 27, 81-85 (2023). MSC: 11G05 11D09 × Cite Format Result Cite Review PDF Full Text: DOI
Kalman, Dan; Mena, Robert A tale of two by two matrices. (English) Zbl 1533.11067 Am. Math. Mon. 130, No. 9, 837-854 (2023). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11D09 15B36 × Cite Format Result Cite Review PDF Full Text: DOI
Dutto, Simone; Murru, Nadir On the cubic Pell equation over finite fields. (English) Zbl 07745968 Quaest. Math. 46, No. 10, 2109-2128 (2023). Reviewer: Ahmet Tekcan (Bursa) MSC: 11D25 11A07 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bogatyrev, Andrei B.; Gendron, Quentin The number of components of the Pell-Abel equations with primitive solutions of given degree. (English. Russian original) Zbl 1523.30012 Russ. Math. Surv. 78, No. 1, 208-210 (2023); translation from Usp. Mat. Nauk 78, No. 1, 209-210 (2023). MSC: 30C10 34A05 × Cite Format Result Cite Review PDF Full Text: DOI MNR
Gawron, Filip; Kobos, Tomasz On length of the period of the continued fraction of \(n \sqrt{d}\). (English) Zbl 1531.11010 Int. J. Number Theory 19, No. 9, 2089-2099 (2023). Reviewer: Anton Shutov (Vladimir) MSC: 11A55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Luca, Florian; Zottor, Faith S. On \(Y\)-coordinates of Pell equations which are Fibonacci numbers. (English) Zbl 1527.11028 Bol. Soc. Mat. Mex., III. Ser. 29, No. 2, Paper No. 49, 43 p. (2023). Reviewer: Mahadi Ddamulira (Kampala) MSC: 11D61 11B39 11D45 × Cite Format Result Cite Review PDF Full Text: DOI
El-Sayed, Adel Abd Elaziz Pell-Lucas polynomials for numerical treatment of the nonlinear fractional-order Duffing equation. (English) Zbl 1529.65010 Demonstr. Math. 56, Article ID 20220220, 17 p. (2023). MSC: 65L05 11B39 34A08 34C15 41A25 × Cite Format Result Cite Review PDF Full Text: DOI
Taghipour, M.; Aminikhah, H. Application of Pell collocation method for solving the general form of time-fractional Burgers equations. (English) Zbl 1512.65233 Math. Sci., Springer 17, No. 2, 183-201 (2023). MSC: 65M70 65R10 34K37 45J05 × Cite Format Result Cite Review PDF Full Text: DOI
Akbary, Amir; Francis, Forrest J. Ambiguous solutions of a Pell equation. (English) Zbl 1533.11066 Involve 16, No. 1, 13-25 (2023). Reviewer: Yasutsugu Fujita (Narashino) MSC: 11D09 × Cite Format Result Cite Review PDF Full Text: DOI
Hu, Yongzhong; Le, Maohua On the \(X\)-coordinates of Pell equations of the form \(px^2\). (English) Zbl 1538.11044 Period. Math. Hung. 86, No. 1, 281-288 (2023). Reviewer: István Gaál (Debrecen) MSC: 11B39 11D09 11D25 × Cite Format Result Cite Review PDF Full Text: DOI
Park, Jinseo Complete solution of Diophantine pairs induced by some Fibonacci formula. (English) Zbl 1523.11036 Algebra Colloq. 30, No. 1, 121-132 (2023). MSC: 11B39 11D09 11D45 11J86 × Cite Format Result Cite Review PDF Full Text: DOI
Cotan, Paul; Teşeleanu, George Continued fractions applied to a family of RSA-like cryptosystems. (English) Zbl 1528.94039 Su, Chunhua (ed.) et al., Information security practice and experience. 17th international conference, ISPEC 2022, Taipei, Taiwan, November 23–25, 2022. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 13620, 589-605 (2022). MSC: 94A60 11A55 11T71 × Cite Format Result Cite Review PDF Full Text: DOI
Chambert-Loir, Antoine On two Olympiad exercises. A walk in number theory. (À propos de deux exercices d’olympiades. Petite promenade en théorie des nombres.) (French. English summary) Zbl 1527.11025 Quadrature 123, 28-32 (2022). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11D09 × Cite Format Result Cite Review PDF
Taghipour, M.; Aminikhah, H. A spectral collocation method based on fractional Pell functions for solving time-fractional Black-Scholes option pricing model. (English) Zbl 1507.91238 Chaos Solitons Fractals 163, Article ID 112571, 10 p. (2022). MSC: 91G60 91G20 35R11 65M70 65M06 × Cite Format Result Cite Review PDF Full Text: DOI
Erduvan, F.; Keskin, R. Pell and Pell-Lucas numbers as product of two repdigits. (English) Zbl 1506.11026 Math. Notes 112, No. 6, 861-871 (2022). Reviewer: Mahadi Ddamulira (Kampala) MSC: 11B39 11D45 11J86 × Cite Format Result Cite Review PDF Full Text: DOI
Zhang, Yong; Tang, Qiongzhi; Zhang, Yuna On the Diophantine equations \(z^2=f(x)^2 \pm f(y)^2\) involving Laurent polynomials. II. (English) Zbl 1503.11076 Miskolc Math. Notes 23, No. 2, 1023-1036 (2022). MSC: 11D72 11D25 11D41 11G05 × Cite Format Result Cite Review PDF Full Text: DOI
Kannan, J.; Mahalakshmi, M.; Deepshika, A. Cryptographic algorithm involving the matrix \(Q^{p*}\). (English) Zbl 1515.94077 Korean J. Math. 30, No. 3, 533-538 (2022). MSC: 94A60 11B39 11T71 11D09 × Cite Format Result Cite Review PDF Full Text: DOI
Tekcan, Ahmet; Biberoğlu, Gülşah The set of automorphisms of Pell forms and Pell equations. (English) Zbl 1513.11096 Southeast Asian Bull. Math. 46, No. 6, 783-800 (2022). MSC: 11D09 11D45 × Cite Format Result Cite Review PDF Full Text: Link
Edjeou, Bilizimbéyé; Faye, Bernadette; Gómez, Carlos A.; Luca, Florian On \(Y\)-coordinates of Pell equations which are Lucas numbers. (English) Zbl 1506.11043 Ramanujan J. 59, No. 4, 1091-1136 (2022). Reviewer: Mahadi Ddamulira (Kampala) MSC: 11D61 11B39 11D45 × Cite Format Result Cite Review PDF Full Text: DOI
Habeb, Jebrel M. Some properties of balancing numbers. (English) Zbl 1501.11022 Jordan J. Math. Stat. 15, No. 3B, 773-785 (2022). MSC: 11B37 11B39 11B83 × Cite Format Result Cite Review PDF
Hilmer, Kieran; Lycan, Ron; Ponomarenko, Vadim Odds inversion problem with replacement. (English) Zbl 1520.11038 Am. Math. Mon. 129, No. 9, 885 (2022). MSC: 11D09 × Cite Format Result Cite Review PDF Full Text: DOI
Choi, Stephen; Tarnu, Daniel The order of the fundamental solution of \(x^2 -Dy^2 =1\) in \(\mathbb{Z}[\sqrt{D}]/\langle D \rangle\). (English) Zbl 1501.11044 Integers 22, Paper A84, 23 p. (2022). MSC: 11D09 × Cite Format Result Cite Review PDF Full Text: Link
Gendron, Quentin Pell-Abel equation and applications. (Équation de Pell-Abel et applications.) (French. English summary) Zbl 1504.30055 C. R., Math., Acad. Sci. Paris 360, 975-992 (2022). MSC: 30F30 30C30 14H40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Aebi, Christian; Cairns, Grant Lattice equable qadrilaterals. II: Kites, trapezoids and cyclic quadrilaterals. (English) Zbl 1513.51065 Int. J. Geom. 11, No. 2, 5-27 (2022). MSC: 51M25 11D09 × Cite Format Result Cite Review PDF Full Text: arXiv Link
Relhan, Priyanka; Verma, Vipin On solutions of the Diophantine equation \(\mathcal{Q}_{\mathfrak{n}} = \mathcal{Q}_{\mathfrak{m}} = 2^{\mathfrak{a}}\). (English) Zbl 1513.11059 JP J. Algebra Number Theory Appl. 55, 9-21 (2022). MSC: 11B39 11D99 × Cite Format Result Cite Review PDF Full Text: DOI
Ait-Amrane, Lyes; Behloul, Djilali; Djoumakh, Akila Diophantine equations involving the bi-periodic Fibonacci and Lucas sequences. (English) Zbl 1497.11069 Acta Comment. Univ. Tartu. Math. 26, No. 1, 129-152 (2022). Reviewer: Mahadi Ddamulira (Kampala) MSC: 11D09 11D45 11B37 11B39 × Cite Format Result Cite Review PDF Full Text: DOI
Stevenhagen, Peter Redei reciprocity, governing fields and negative Pell. (English) Zbl 1514.11073 Math. Proc. Camb. Philos. Soc. 172, No. 3, 627-654 (2022). Reviewer: Abdelmalek Azizi (Oujda) MSC: 11R11 11R37 11R16 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Şiar, Z.; Keskin, R. On the exponential Diophantine equation \((a^n-2)(b^n-2)=x^2\). (English) Zbl 1496.11058 Math. Notes 111, No. 6, 903-912 (2022). Reviewer: Anitha Srinivasan (Madrid) MSC: 11D61 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Hajdu, L.; Sebestyén, P. Terms of recurrence sequences in the solution sets of generalized Pell equations. (English) Zbl 1501.11045 Int. J. Number Theory 18, No. 7, 1605-1612 (2022). Reviewer: Clemens Fuchs (Salzburg) MSC: 11D09 11D61 11B39 × Cite Format Result Cite Review PDF Full Text: DOI
Taghipour, M.; Aminikhah, H. A fast collocation method for solving the weakly singular fractional integro-differential equation. (English) Zbl 1499.65355 Comput. Appl. Math. 41, No. 4, Paper No. 142, 38 p. (2022). MSC: 65L60 65L20 45J05 34K37 × Cite Format Result Cite Review PDF Full Text: DOI
García, Jonathan; Gómez, Carlos A. On a variant of Pillai problem: integers as difference between generalized Pell numbers and perfect powers. (English) Zbl 1490.11024 Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 116, No. 3, Paper No. 103, 36 p. (2022). Reviewer: Mahadi Ddamulira (Kampala) MSC: 11B39 11D45 11D61 11J86 × Cite Format Result Cite Review PDF Full Text: DOI
Szechtman, Fernando Closed formulae for certain Fermat-Pell equations. (English) Zbl 1493.11161 Commun. Algebra 50, No. 2, 661-667 (2022). Reviewer: Anitha Srinivasan (Madrid) MSC: 11Y65 11A55 11D09 11Y50 11B37 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Fu, Ruiqin; Yang, Hai On the generalized Ramanujan-Nagell equation \(x^2+(3m^2+1)=(4m^2+1)^n\). (English) Zbl 1492.11075 Indian J. Pure Appl. Math. 53, No. 1, 222-227 (2022). Reviewer: Anitha Srinivasan (Madrid) MSC: 11D61 × Cite Format Result Cite Review PDF Full Text: DOI
Bazzanella, Danilo; Di Scala, Antonio; Dutto, Simone; Murru, Nadir Primality tests, linear recurrent sequences and the Pell equation. (English) Zbl 1486.11159 Ramanujan J. 57, No. 2, 755-768 (2022). Reviewer: Juan Tena Ayuso (Valladolid) MSC: 11Y11 11B39 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Alahmadi, Adel; Luca, Florian On the Euler function of \(Y\)-coordinates of Pell equations and repdigits. (English) Zbl 1485.11073 Result. Math. 77, No. 2, Paper No. 59, 6 p. (2022). Reviewer: Jaroslav Hančl (Ostrava) MSC: 11D61 11A25 11B39 11A63 × Cite Format Result Cite Review PDF Full Text: DOI
Togbé, A.; Walsh, P. G. A classical approach to a parametric family of simultaneous Pell equations with applications to a family of Thue equations. (English) Zbl 1486.11048 Bol. Soc. Mat. Mex., III. Ser. 28, No. 1, Paper No. 4, 7 p. (2022). Reviewer: Maciej Ulas (Kraków) MSC: 11D25 11D59 × Cite Format Result Cite Review PDF Full Text: DOI
Alkabouss, Sakha A.; Benseba, Boualem; Berbara, Nacira; Earp-Lynch, Simon; Luca, Florian A note on the Diophantine equation \(x^2-kxy+ky^2+ly=0\). (English) Zbl 07857986 Mathematica 63(86), No. 2, 151-157 (2021). MSC: 11D09 × Cite Format Result Cite Review PDF Full Text: DOI
Çağman, Abdullah; Polat, Kadirhan On a Diophantine equation related to the difference of two Pell numbers. (English) Zbl 1538.11105 Contrib. Math. 3, 37-42 (2021). MSC: 11D61 11J86 11B37 11B39 × Cite Format Result Cite Review PDF Full Text: DOI
Kuděj, Martin Continued fractions with prescribed period. (Czech) Zbl 1538.11022 Pokroky Mat. Fyz. Astron. 66, No. 1, 11-32 (2021). Reviewer: Štěpán Holub (Praha) MSC: 11A55 11D09 × Cite Format Result Cite Review PDF Full Text: Link
Andrica, Dorin; Bagdasar, Ovidiu; Ţurcaş, George Cătălin On some new results for the generalised Lucas sequences. (English) Zbl 1524.11031 An. Științ. Univ. “Ovidius” Constanța, Ser. Mat. 29, No. 1, 17-36 (2021). MSC: 11B39 26C05 × Cite Format Result Cite Review PDF Full Text: DOI
Tekcan, Ahmet; Aydın, Samet On \(t\)-balancers, \(t\)-balancing numbers and Lucas \(t\)-balancing numbers. (English) Zbl 1518.11015 Lib. Math. (N.S.) 41, No. 1, 37-51 (2021). MSC: 11B37 11B39 11D09 × Cite Format Result Cite Review PDF
Cantone, Domenico; Omodeo, Eugenio G. “One equation to rule them all”, revisited. (English) Zbl 1539.11151 Rend. Ist. Mat. Univ. Trieste 53, Paper No. 28, 32 p. (2021). MSC: 11U05 03D25 03D80 11D25 × Cite Format Result Cite Review PDF Full Text: DOI
Rack, Heinz-Joachim; Vajda, Robert An explicit radical parametrization of Zolotarev polynomials of degree 7 in terms of nested square roots. (English) Zbl 1487.41006 Adv. Stud.: Euro-Tbil. Math. J. 14, No. 4, 37-60 (2021). MSC: 41A10 14Q05 68W30 41A50 × Cite Format Result Cite Review PDF Full Text: Link
Ganesh, Ashokan Hari; Prabhakaran, Kumaresan On the integral solutions of binary quadratic Diophantine equation \(ax^2-bx=cy^2\). (English) Zbl 1499.11163 South East Asian J. Math. Math. Sci. 17, No. 2, 337-354 (2021). MSC: 11D09 × Cite Format Result Cite Review PDF Full Text: Link
Diaz-Vargas, Javier; Hernández-Ketchul, Myriam; Rubio-Barrios, Carlos Jacob On the solutions of the Pell-type equation \(x^2-ry^2=r\) in the ring of Gaussian integers \(\mathbb{Z}[i]\) with \(r\) a Gaussian prime. (English) Zbl 1499.11161 JP J. Algebra Number Theory Appl. 50, No. 1, 19-43 (2021). MSC: 11D09 11R11 × Cite Format Result Cite Review PDF Full Text: DOI
Çağman, A. An approach to Pillai’s problem with the Pell sequence and the powers of 3. (English) Zbl 1499.11051 Miskolc Math. Notes 22, No. 2, 599-610 (2021). MSC: 11B39 11J86 × Cite Format Result Cite Review PDF Full Text: DOI
Zhang, Zhongfeng; Togbé, Alain On the Ramanujan-Nagell type Diophantine equation \(Dx^2+k^n=B\). (English) Zbl 1493.11071 Glas. Mat., III. Ser. 56, No. 2, 263-270 (2021). Reviewer: Maciej Ulas (Kraków) MSC: 11D41 11D61 × Cite Format Result Cite Review PDF Full Text: DOI
Adegbindin, Chefiath Awero; Luca, Florian; Togbé, Alain Pell and Pell-Lucas numbers as sums of three repdigits. (English) Zbl 1484.11006 Acta Math. Univ. Comen., New Ser. 90, No. 1, 7-25 (2021). Reviewer: Mahadi Ddamulira (Kampala) MSC: 11A25 11B39 11J86 × Cite Format Result Cite Review PDF Full Text: Link
Conrey, J. B.; Holmstrom, M. A. Smooth values of quadratic polynomials. (English) Zbl 1487.11085 Exp. Math. 30, No. 4, 447-452 (2021). Reviewer: Andrej Dujella (Zagreb) MSC: 11N36 11D09 × Cite Format Result Cite Review PDF Full Text: DOI
Cantone, D.; Casagrande, A.; Fabris, F.; Omodeo, E. The quest for Diophantine finite-fold-ness. (English) Zbl 1547.03275 Matematiche 76, No. 1, 133-160 (2021). MSC: 03D25 03D35 03D80 11D85 × Cite Format Result Cite Review PDF Full Text: DOI
Kerins, Bowen; Yong, Darryl; Cuoco, Al; Stevens, Glenn Fractions: to be continued. (English) Zbl 1497.11002 IAS/PCMI. The Teacher Program Series 8. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-6293-2/pbk; 978-1-4704-6820-0/ebook). xi, 126 p. (2021). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11-01 11A55 × Cite Format Result Cite Review PDF
Zhang, Yong; Gao, Dan On certain Diophantine equations concerning the area of right triangles. (English) Zbl 1478.51009 Math. Slovaca 71, No. 1, 171-182 (2021). MSC: 51M25 11D25 11D72 × Cite Format Result Cite Review PDF Full Text: DOI
Erazo, Harold S.; Gómez, Carlos An exponential Diophantine equation related to the sum of powers of two consecutive terms of a Lucas sequence and \(x\)-coordinates of Pell equations. (English) Zbl 1499.11060 Period. Math. Hung. 83, No. 2, 165-184 (2021). Reviewer: Oto Strauch (Bratislava) MSC: 11B39 11J86 × Cite Format Result Cite Review PDF Full Text: DOI
Erazo, Harold S.; Gómez, Carlos A.; Luca, Florian On Pillai’s problem with \(X\)-coordinates of Pell equations and powers of 2. II. (English) Zbl 1493.11074 Int. J. Number Theory 17, No. 10, 2251-2277 (2021). Reviewer: Ilker Inam (Bilecik) MSC: 11D61 11B39 11D45 × Cite Format Result Cite Review PDF Full Text: DOI
Bychkov, Boris Sergeevich; Shabat, Georgiĭ Borisovich On generalizations of Chebyshev polynomials and Catalan numbers. (Russian. English translation) Zbl 1513.39052 Ufim. Mat. Zh. 13, No. 2, 11-17 (2021); translation in Ufa Math. J. 13, No. 2, 8-14 (2021). MSC: 39A70 11B83 33C45 11B37 × Cite Format Result Cite Review PDF Full Text: DOI MNR
Zheng, Mengce; Kunihiro, Noboru; Yao, Yuanzhi Cryptanalysis of the RSA variant based on cubic Pell equation. (English) Zbl 1517.94173 Theor. Comput. Sci. 889, 135-144 (2021). MSC: 94A60 × Cite Format Result Cite Review PDF Full Text: DOI
Lin, Lijuan On the Diophantine equation \(7x(x + 1)(x + 2)(x + 3) = 5y(y + 1)(y + 2)(y + 3)\). (Chinese. English summary) Zbl 1488.11083 Math. Pract. Theory 51, No. 9, 218-223 (2021). MSC: 11D25 × Cite Format Result Cite Review PDF
Yang, Shichun; Liao, Qunying The determinant of a class of irreducible polynomials over \(\mathbb{Z}[\zeta_m]\) related to lattice-based diagonal space-time block codes. (Chinese. English summary) Zbl 1488.94124 Chin. Ann. Math., Ser. A 42, No. 2, 149-158 (2021). MSC: 94B75 94B60 11H71 × Cite Format Result Cite Review PDF Full Text: DOI
Zhang, Y. On products of consecutive arithmetic progressions. III. (English) Zbl 1480.11035 Acta Math. Hung. 163, No. 2, 407-428 (2021). Reviewer: Maciej Ulas (Kraków) MSC: 11D25 11D72 × Cite Format Result Cite Review PDF Full Text: DOI
Bliznac Trebješanin, M. Extension of a Diophantine triple with the property \(D(4)\). (English) Zbl 1488.11075 Acta Math. Hung. 163, No. 1, 213-246 (2021). MSC: 11D09 11D45 11J86 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Matthews, Keith R.; Robertson, John P. On solving a binary quadratic Diophantine equation. (English) Zbl 1483.11056 Rocky Mt. J. Math. 51, No. 4, 1369-1385 (2021). MSC: 11D09 11D85 × Cite Format Result Cite Review PDF
Susilo, Willy; Tonien, Joseph A Wiener-type attack on an RSA-like cryptosystem constructed from cubic Pell equations. (English) Zbl 1517.94159 Theor. Comput. Sci. 885, 125-130 (2021). MSC: 94A60 11T71 × Cite Format Result Cite Review PDF Full Text: DOI
Gupta, S. \(D(-1)\) tuples in imaginary quadratic fields. (English) Zbl 1488.11077 Acta Math. Hung. 164, No. 2, 556-569 (2021). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 11D09 11R11 11J68 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Walsh, P. G. Corrigendum to: “On two classes of simultaneous Pell equations with no solutions”. (English) Zbl 1464.11034 Math. Comput. 90, No. 331, 2503-2505 (2021). MSC: 11D09 × Cite Format Result Cite Review PDF Full Text: DOI
Boca, Florin P.; Siskaki, Maria Distribution of periodic points of certain Gauss shifts with infinite invariant measure. (English) Zbl 1473.37007 Nonlinearity 34, No. 7, 4570-4603 (2021). MSC: 37A44 37C25 11J70 11N37 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Cohen, Boaz Chebyshev polynomials and Pell equations over finite fields. (English) Zbl 07361081 Czech. Math. J. 71, No. 2, 491-510 (2021). Reviewer: Andrej Dujella (Zagreb) MSC: 11D09 12E20 11T06 × Cite Format Result Cite Review PDF Full Text: DOI
Tchammou, Euloge; Togbé, Alain On some Diophantine equations involving balancing numbers. (English) Zbl 1524.11047 Arch. Math., Brno 57, No. 2, 113-130 (2021). MSC: 11B39 11B83 11D99 × Cite Format Result Cite Review PDF Full Text: DOI
Bridgeman, Martin Dilogarithm identities for solutions to Pell’s equation in terms of continued fraction convergents. (English) Zbl 1483.11050 Ramanujan J. 55, No. 1, 141-161 (2021). MSC: 11D09 11A55 33B30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ddamulira, Mahadi On the \(x\)-coordinates of Pell equations that are sums of two Padovan numbers. (English) Zbl 1471.11064 Bol. Soc. Mat. Mex., III. Ser. 27, No. 1, Paper No. 4, 23 p. (2021). MSC: 11B39 11D45 11D61 11J86 × Cite Format Result Cite Review PDF Full Text: DOI
Hoelscher, Zachary Semicomplete arithmetic sequences, division of hypercubes, and the Pell constant. (English) Zbl 1462.05030 PUMP J. Undergrad. Res. 4, 108-116 (2021). MSC: 05A17 05A30 11B65 × Cite Format Result Cite Review PDF Full Text: arXiv Link
Korobov, Alekseĭ Aleksandrovich; Korobov, Oleg Alekseevich On the discriminant of a quadratic field with intermediate fractions of negative norm and the decomposability of its representing polynomial. (Russian. English summary) Zbl 1482.11040 Sib. Èlektron. Mat. Izv. 18, No. 1, 319-331 (2021). MSC: 11D09 × Cite Format Result Cite Review PDF Full Text: DOI
Hoque, Azizul; Kotyada, Srinivas Class number one problem for the real quadratic fields \(\mathbb{Q}(\sqrt{m^2+2r})\). (English) Zbl 1468.11226 Arch. Math. 116, No. 1, 33-36 (2021). Reviewer: Elliot Benjamin (Winterport) MSC: 11R29 11R11 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Hashim, Hayder R. Solutions of the Diophantine equation \(7X^2 + Y^7 = Z^2\) from recurrence sequences. (English) Zbl 1483.11061 Commun. Math. 28, No. 1, 55-66 (2020). MSC: 11D41 11B39 × Cite Format Result Cite Review PDF Full Text: DOI
Qu, Yunyun On the common solution of the simultaneous Diophantine equations \({x^2} - 18{y^2} = 1\) and \({y^2} - b z^2 = 16\). (Chinese. English summary) Zbl 1474.11082 J. Northeast Norm. Univ., Nat. Sci. Ed. 52, No. 4, 1-5 (2020). MSC: 11D09 × Cite Format Result Cite Review PDF Full Text: DOI