Tadee, Suton On the Diophantine equation \(\frac{1}{a}+\frac{1}{b}=\frac{m}{pq}\). (English) Zbl 07774204 Int. J. Math. Comput. Sci. 19, No. 2, 373-375 (2024). MSC: 11D85 11D99 PDFBibTeX XMLCite \textit{S. Tadee}, Int. J. Math. Comput. Sci. 19, No. 2, 373--375 (2024; Zbl 07774204) Full Text: Link
Valencia, Carlos E.; Villagrán, Ralihe R. Arithmetical structures on dominated polynomials. (English) Zbl 07713856 São Paulo J. Math. Sci. 17, No. 1, 430-439 (2023). MSC: 11D72 11Y50 11C20 15B48 PDFBibTeX XMLCite \textit{C. E. Valencia} and \textit{R. R. Villagrán}, São Paulo J. Math. Sci. 17, No. 1, 430--439 (2023; Zbl 07713856) Full Text: DOI arXiv
Walsh, P. G. An observation concerning the representation of positive integers as a sum of three cubes. (English) Zbl 1523.11234 Rocky Mt. J. Math. 53, No. 1, 241-248 (2023). Reviewer: Anitha Srinivasan (Madrid) MSC: 11Y50 11D85 11D25 PDFBibTeX XMLCite \textit{P. G. Walsh}, Rocky Mt. J. Math. 53, No. 1, 241--248 (2023; Zbl 1523.11234) Full Text: DOI Link
Tadee, Suton; Poopra, Sudaporn On the Diophantine equation \(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{1}{n}\). (English) Zbl 1524.11092 Int. J. Math. Comput. Sci. 18, No. 2, 173-177 (2023). MSC: 11D68 PDFBibTeX XMLCite \textit{S. Tadee} and \textit{S. Poopra}, Int. J. Math. Comput. Sci. 18, No. 2, 173--177 (2023; Zbl 1524.11092) Full Text: Link
Yuan, Xiaodan A Diophantine equation and its positive integer solutions. (English) Zbl 1513.11118 JP J. Algebra Number Theory Appl. 56, 37-69 (2022). MSC: 11D68 PDFBibTeX XMLCite \textit{X. Yuan}, JP J. Algebra Number Theory Appl. 56, 37--69 (2022; Zbl 1513.11118) Full Text: DOI
Valencia, Carlos E.; Villagrán, Ralihe R. Algorithmic aspects of arithmetical structures. (English) Zbl 1493.11077 Linear Algebra Appl. 640, 191-208 (2022). Reviewer: Scott Corry (Appleton) MSC: 11D72 11Y50 11C20 15B48 PDFBibTeX XMLCite \textit{C. E. Valencia} and \textit{R. R. Villagrán}, Linear Algebra Appl. 640, 191--208 (2022; Zbl 1493.11077) Full Text: DOI arXiv
Luo, Jiagui Perfect powers of five with few ternary digits. (Chinese. English summary) Zbl 1513.11102 Chin. Ann. Math., Ser. A 42, No. 4, 359-378 (2021). MSC: 11D41 11D61 PDFBibTeX XMLCite \textit{J. Luo}, Chin. Ann. Math., Ser. A 42, No. 4, 359--378 (2021; Zbl 1513.11102) Full Text: DOI
Li, Yang On the positive integer solutions of the simultaneous Diophantine equations \(8{x^2} - 6{y^2} = 2\) and \(28{y^2} - 8{z^2} = 20\). (Chinese. English summary) Zbl 1488.11080 Math. Pract. Theory 51, No. 15, 300-303 (2021). MSC: 11D09 PDFBibTeX XMLCite \textit{Y. Li}, Math. Pract. Theory 51, No. 15, 300--303 (2021; Zbl 1488.11080)
Zheng, Hui; Yang, Shichun The positive integer solutions to multivariate Euler function equation \(\varphi(x_1x_2 \cdots x_n) = k_1\varphi(x_1) + k_2\varphi(x_2) + \cdots + k_n\varphi(x_n) \pm l\). (Chinese. English summary) Zbl 1488.11014 Math. Pract. Theory 51, No. 13, 313-318 (2021). MSC: 11A25 11D45 PDFBibTeX XMLCite \textit{H. Zheng} and \textit{S. Yang}, Math. Pract. Theory 51, No. 13, 313--318 (2021; Zbl 1488.11014)
Zhang, Sibao; Jiang, Lianxia The solutions of arithmetic function equation \(k\varphi(Y) = {\varphi_2}(Y) + S(Y^8)\). (Chinese. English summary) Zbl 1488.11013 J. Jiangxi Norm. Univ., Nat. Sci. Ed. 45, No. 2, 194-197 (2021). MSC: 11A25 11D41 PDFBibTeX XMLCite \textit{S. Zhang} and \textit{L. Jiang}, J. Jiangxi Norm. Univ., Nat. Sci. Ed. 45, No. 2, 194--197 (2021; Zbl 1488.11013) Full Text: DOI
Zhang, Sibao; Jiang, Lianxia Discussion on the positive integer solution of equation \(k\varphi (m) = S(m^t)\). (Chinese. English summary) Zbl 1488.11012 J. Henan Univ., Nat. Sci. 51, No. 3, 367-372 (2021). MSC: 11A25 11D41 PDFBibTeX XMLCite \textit{S. Zhang} and \textit{L. Jiang}, J. Henan Univ., Nat. Sci. 51, No. 3, 367--372 (2021; Zbl 1488.11012) Full Text: DOI
Guan, Xungui A conjecture of Jeśmanowicz concerning Pythagorean triples. (Chinese. English summary) Zbl 1488.11092 Adv. Math., Beijing 50, No. 4, 519-528 (2021). MSC: 11D61 PDFBibTeX XMLCite \textit{X. Guan}, Adv. Math., Beijing 50, No. 4, 519--528 (2021; Zbl 1488.11092)
Cai, Tianxin; Zhang, Yong A variety of Euler’s sum of powers conjecture. (English) Zbl 07442476 Czech. Math. J. 71, No. 4, 1099-1113 (2021). MSC: 11D72 11D41 11G05 PDFBibTeX XMLCite \textit{T. Cai} and \textit{Y. Zhang}, Czech. Math. J. 71, No. 4, 1099--1113 (2021; Zbl 07442476) 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 PDFBibTeX XMLCite \textit{L. Lin}, Math. Pract. Theory 51, No. 9, 218--223 (2021; Zbl 1488.11083)
Deng, Naijuan Number of solutions to \({(an)^x} + {(bn)^y} = {(cn)^z}\). (Chinese. English summary) Zbl 1488.11091 Math. Pract. Theory 51, No. 9, 194-204 (2021). MSC: 11D61 PDFBibTeX XMLCite \textit{N. Deng}, Math. Pract. Theory 51, No. 9, 194--204 (2021; Zbl 1488.11091)
Guan, Xungui On the Diophantine equation \(X^2 - (a^2 + 1)Y^4 = k^2 - 1 - 2ka\). (Chinese. English summary) Zbl 1488.11081 J. Sichuan Norm. Univ., Nat. Sci. 44, No. 2, 225-234 (2021). MSC: 11D25 11J68 PDFBibTeX XMLCite \textit{X. Guan}, J. Sichuan Norm. Univ., Nat. Sci. 44, No. 2, 225--234 (2021; Zbl 1488.11081) 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 PDFBibTeX XMLCite \textit{Y. Zhang}, Acta Math. Hung. 163, No. 2, 407--428 (2021; Zbl 1480.11035) Full Text: DOI
Tong, Ruizhou On the Diophantine equation \((2^x-1)(p^y-1)=2z^2\). (English) Zbl 1513.11115 Czech. Math. J. 71, No. 3, 689-696 (2021). MSC: 11D61 PDFBibTeX XMLCite \textit{R. Tong}, Czech. Math. J. 71, No. 3, 689--696 (2021; Zbl 1513.11115) Full Text: DOI
Deng, Guilin; Liao, Qunying The solvability of the equation \({\varphi_e}(n) = {p^{t\omega (n)}}(e = 2, 3, 4, 6)\). (Chinese. English summary) Zbl 1474.11008 J. Sichuan Norm. Univ., Nat. Sci. 44, No. 1, 18-22 (2021). MSC: 11A25 PDFBibTeX XMLCite \textit{G. Deng} and \textit{Q. Liao}, J. Sichuan Norm. Univ., Nat. Sci. 44, No. 1, 18--22 (2021; Zbl 1474.11008) Full Text: DOI
Xie, Tiantian; Yang, Hai; Xu, Qian The positive integer solutions of elliptic curves \({y^2} = qx ({x^2} - 256)\). (Chinese. English summary) Zbl 1474.11087 J. Qufu Norm. Univ., Nat. Sci. 47, No. 1, 47-51 (2021). MSC: 11D25 11G05 11G07 PDFBibTeX XMLCite \textit{T. Xie} et al., J. Qufu Norm. Univ., Nat. Sci. 47, No. 1, 47--51 (2021; Zbl 1474.11087)
Zhang, Sibao The solution of a quaternary variable coefficient mixed equation on Euler function \(\varphi (n)\). (Chinese. English summary) Zbl 1474.11019 J. Cent. China Norm. Univ., Nat. Sci. 55, No. 1, 24-29 (2021). MSC: 11A25 PDFBibTeX XMLCite \textit{S. Zhang}, J. Cent. China Norm. Univ., Nat. Sci. 55, No. 1, 24--29 (2021; Zbl 1474.11019) Full Text: DOI
Deng, Naijuan; Yuan, Pingzhi Diophantine equation \(((c + 1)m^2 + 1)^x + (cm^2 - 1)^y = (am)^z\). (Chinese. English summary) Zbl 1474.11095 Math. Pract. Theory 50, No. 20, 220-226 (2020). MSC: 11D61 PDFBibTeX XMLCite \textit{N. Deng} and \textit{P. Yuan}, Math. Pract. Theory 50, No. 20, 220--226 (2020; Zbl 1474.11095)
Kaidireya, Nuermaimaiti; Zhang, Sibao Discussion of solutions of an equation on the number-theoretic function \(\varphi(m)\). (Chinese. English summary) Zbl 1463.11107 Pure Appl. Math. 36, No. 2, 229-238 (2020). MSC: 11D72 11D45 PDFBibTeX XMLCite \textit{N. Kaidireya} and \textit{S. Zhang}, Pure Appl. Math. 36, No. 2, 229--238 (2020; Zbl 1463.11107) Full Text: DOI
Li, Yuan; Luo, Jiagui Extension of the Stormer theorem. (Chinese. English summary) Zbl 1463.11100 J. Nat. Sci. Heilongjiang Univ. 37, No. 2, 167-172 (2020). MSC: 11D09 PDFBibTeX XMLCite \textit{Y. Li} and \textit{J. Luo}, J. Nat. Sci. Heilongjiang Univ. 37, No. 2, 167--172 (2020; Zbl 1463.11100) Full Text: DOI
Deng, Guilin; Liao, Qunying The solvability of the equation \({\varphi_e} (n) = 2^{t\omega (n)}\). (Chinese. English summary) Zbl 1463.11006 J. Sichuan Norm. Univ., Nat. Sci. 43, No. 2, 187-201 (2020). MSC: 11A25 11B68 11Y70 PDFBibTeX XMLCite \textit{G. Deng} and \textit{Q. Liao}, J. Sichuan Norm. Univ., Nat. Sci. 43, No. 2, 187--201 (2020; Zbl 1463.11006) Full Text: DOI
Guan, Xungui On the Diophantine equation \(x^2-2y^4=M (M=17, 41, 73, 89, 97)\). (Chinese. English summary) Zbl 1463.11103 J. Cent. China Norm. Univ., Nat. Sci. 54, No. 2, 200-206 (2020). MSC: 11D25 PDFBibTeX XMLCite \textit{X. Guan}, J. Cent. China Norm. Univ., Nat. Sci. 54, No. 2, 200--206 (2020; Zbl 1463.11103) Full Text: DOI
Zhang, Mingli; Gao, Li On the positive integer solution of a ternary variable coefficient Euler function equation. (Chinese. English summary) Zbl 1463.11013 J. Cent. China Norm. Univ., Nat. Sci. 54, No. 1, 23-29 (2020). MSC: 11A25 11D72 PDFBibTeX XMLCite \textit{M. Zhang} and \textit{L. Gao}, J. Cent. China Norm. Univ., Nat. Sci. 54, No. 1, 23--29 (2020; Zbl 1463.11013) Full Text: DOI
Guan, Xungui On the Diophantine equation \(X^2 + 4Y^4 = pZ^4\). (Chinese. English summary) Zbl 1449.11057 Math. Pract. Theory 49, No. 18, 279-284 (2019). MSC: 11D25 PDFBibTeX XMLCite \textit{X. Guan}, Math. Pract. Theory 49, No. 18, 279--284 (2019; Zbl 1449.11057)
Shen, Jianghong; Gao, Li; Zhang, Mingli Solvability of a ternary variable coefficient of Euler functional equation with constant terms and a perfect number. (Chinese. English summary) Zbl 1449.11009 J. Yunnan Minzu Univ., Nat. Sci. 28, No. 5, 455-461 (2019). MSC: 11A25 PDFBibTeX XMLCite \textit{J. Shen} et al., J. Yunnan Minzu Univ., Nat. Sci. 28, No. 5, 455--461 (2019; Zbl 1449.11009)
Li, Jianglong; Luo, Ming; Lin, Lijuan On the positive integer solution of Diophantine equation \(x (x+1) (x+2) (x+3) = 42y (y+1) (y+2) (y+3)\). (Chinese. English summary) Zbl 1449.11058 Basic Sci. J. Text. Univ. 32, No. 3, 293-297 (2019). MSC: 11D25 PDFBibTeX XMLCite \textit{J. Li} et al., Basic Sci. J. Text. Univ. 32, No. 3, 293--297 (2019; Zbl 1449.11058) Full Text: DOI
Zhu, Jie; Liao, Qunying The solvability of the equation \(Z (n) = \varphi_e(\mathrm{SL}(n))\). (Chinese. English summary) Zbl 1449.11016 Adv. Math., Beijing 48, No. 5, 541-554 (2019). MSC: 11A25 PDFBibTeX XMLCite \textit{J. Zhu} and \textit{Q. Liao}, Adv. Math., Beijing 48, No. 5, 541--554 (2019; Zbl 1449.11016)
Deng, Nai-Juan; Wu, Dan-Yao; Yuan, Ping-Zhi The exponential Diophantine equation \((3am^2-1)^x+(a(a-3)m^2+1)^y=(am)^z\). (English) Zbl 1448.11071 Turk. J. Math. 43, No. 5, 2561-2567 (2019). MSC: 11D61 PDFBibTeX XMLCite \textit{N.-J. Deng} et al., Turk. J. Math. 43, No. 5, 2561--2567 (2019; Zbl 1448.11071) Full Text: Link
Zhang, Sibao; Yoldax, Akim Two equations on generalized Euler function \({\varphi_2} (n)\). (Chinese. English summary) Zbl 1449.11015 J. Northeast Norm. Univ., Nat. Sci. Ed. 51, No. 2, 7-12 (2019). MSC: 11A25 PDFBibTeX XMLCite \textit{S. Zhang} and \textit{A. Yoldax}, J. Northeast Norm. Univ., Nat. Sci. Ed. 51, No. 2, 7--12 (2019; Zbl 1449.11015) Full Text: DOI
Zhang, Sibao Solutions on Euler function equation \(\varphi (n) = {2^{\omega (n)}}{3^{\omega (n)}}{5^{\omega (n)}}\). (Chinese. English summary) Zbl 1449.11014 J. Nanchang Univ., Nat. Sci. 43, No. 2, 114-119 (2019). MSC: 11A25 PDFBibTeX XMLCite \textit{S. Zhang}, J. Nanchang Univ., Nat. Sci. 43, No. 2, 114--119 (2019; Zbl 1449.11014)
Zhang, Sibao Solutions of two equations related to generalized Euler function. (Chinese. English summary) Zbl 1449.11013 J. Anhui Univ., Nat. Sci. 43, No. 4, 32-35 (2019). MSC: 11A25 PDFBibTeX XMLCite \textit{S. Zhang}, J. Anhui Univ., Nat. Sci. 43, No. 4, 32--35 (2019; Zbl 1449.11013) Full Text: DOI
He, Yanfeng On the exponential Diophantine equation \(x^2=D^{2m}-D^mP^n+p^{2n}\). (Chinese. English summary) Zbl 1438.11085 J. Math., Wuhan Univ. 39, No. 2, 279-286 (2019). MSC: 11D61 PDFBibTeX XMLCite \textit{Y. He}, J. Math., Wuhan Univ. 39, No. 2, 279--286 (2019; Zbl 1438.11085) Full Text: DOI
Guan, Xungui On positive integer solutions to the simultaneous Pell equations \({y^2} - D{z^2} = 1\), \({x^2} - 2D{z^2} = 1\). (Chinese. English summary) Zbl 1438.11076 J. Cent. China Norm. Univ., Nat. Sci. 53, No. 2, 171-180 (2019). MSC: 11D09 PDFBibTeX XMLCite \textit{X. Guan}, J. Cent. China Norm. Univ., Nat. Sci. 53, No. 2, 171--180 (2019; Zbl 1438.11076) Full Text: DOI
Zhang, Sibao; Yang, Yanni; Xi, Xiaozhong Several nonlinear equations on Euler function \(\varphi(n)\). (Chinese. English summary) Zbl 1438.11013 J. Henan Univ., Nat. Sci. 49, No. 1, 122-126 (2019). MSC: 11A25 PDFBibTeX XMLCite \textit{S. Zhang} et al., J. Henan Univ., Nat. Sci. 49, No. 1, 122--126 (2019; Zbl 1438.11013) Full Text: DOI
Zhang, Sibao Solutions of two equations mixing Euler function \(\varphi(n)\) with generalized Euler function \(\varphi_2(n)\). (Chinese. English summary) Zbl 1438.11011 J. Beihua Univ., Nat. Sci. 20, No. 1, 8-14 (2019). MSC: 11A25 PDFBibTeX XMLCite \textit{S. Zhang}, J. Beihua Univ., Nat. Sci. 20, No. 1, 8--14 (2019; Zbl 1438.11011) Full Text: DOI
Yang, Hai; Fu, Ruiqin A note on the Goormaghtigh equation. (English) Zbl 1438.11089 Period. Math. Hung. 79, No. 1, 86-93 (2019). Reviewer: Le Maohua (Zhanjiang) MSC: 11D61 11J86 PDFBibTeX XMLCite \textit{H. Yang} and \textit{R. Fu}, Period. Math. Hung. 79, No. 1, 86--93 (2019; Zbl 1438.11089) Full Text: DOI
Liu, Baoli The solvability for a class of the exponential Diophantine equation. (Chinese. English summary) Zbl 1424.11085 Math. Pract. Theory 48, No. 14, 308-311 (2018). MSC: 11D61 PDFBibTeX XMLCite \textit{B. Liu}, Math. Pract. Theory 48, No. 14, 308--311 (2018; Zbl 1424.11085)
Gu, Xiuchuan Existence of solution for the system of Pell equations. (Chinese. English summary) Zbl 1424.11071 J. Cent. China Norm. Univ., Nat. Sci. 52, No. 5, 619-621 (2018). MSC: 11D09 PDFBibTeX XMLCite \textit{X. Gu}, J. Cent. China Norm. Univ., Nat. Sci. 52, No. 5, 619--621 (2018; Zbl 1424.11071) Full Text: DOI
Jiang, Lianxia Positive integer solutions of a nonlinear equation containing Euler function \(\varphi (n)\). (Chinese. English summary) Zbl 1424.11010 J. Beihua Univ., Nat. Sci. 19, No. 6, 719-723 (2018). MSC: 11A25 PDFBibTeX XMLCite \textit{L. Jiang}, J. Beihua Univ., Nat. Sci. 19, No. 6, 719--723 (2018; Zbl 1424.11010) Full Text: DOI
Zheng, Lu; Gao, Li; Guo, Mengyuan Positive integer solution of nonlinear equations related to Euler function \(\varphi \left ( n \right)\). (Chinese. English summary) Zbl 1424.11018 Pure Appl. Math. 34, No. 2, 172-176 (2018). MSC: 11A25 PDFBibTeX XMLCite \textit{L. Zheng} et al., Pure Appl. Math. 34, No. 2, 172--176 (2018; Zbl 1424.11018) Full Text: DOI
Diblík, Josef; Medina, Rigoberto Exact asymptotics of positive solutions to Dickman equation. (English) Zbl 1374.34243 Discrete Contin. Dyn. Syst., Ser. B 23, No. 1, 101-121 (2018). MSC: 34K06 34K25 11N25 11A51 PDFBibTeX XMLCite \textit{J. Diblík} and \textit{R. Medina}, Discrete Contin. Dyn. Syst., Ser. B 23, No. 1, 101--121 (2018; Zbl 1374.34243) Full Text: DOI
Yuan, Xiaodan; Luo, Jiagui On the Diophantine equation \(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{1}{3p}\). (English) Zbl 1425.11061 AIMS Math. 2, No. 1, 111-127 (2017). MSC: 11D68 PDFBibTeX XMLCite \textit{X. Yuan} and \textit{J. Luo}, AIMS Math. 2, No. 1, 111--127 (2017; Zbl 1425.11061) Full Text: DOI
Yang, Hai; Hou, Jing; Fu, Ruiqin On the solvability of the cubic Diophantine equation \({x^3}+1=2{p_1}{p_2}Q{y^2}\). (Chinese. English summary) Zbl 1399.11094 Acta Sci. Nat. Univ. Sunyatseni 56, No. 5, 30-33 (2017). MSC: 11D25 PDFBibTeX XMLCite \textit{H. Yang} et al., Acta Sci. Nat. Univ. Sunyatseni 56, No. 5, 30--33 (2017; Zbl 1399.11094) Full Text: DOI
Bai, Jiwen; Zhao, Xiqing Several equations related to the Euler function \(\varphi \left ( n \right)\). (Chinese. English summary) Zbl 1399.11058 J. Yunnan Minzu Univ., Nat. Sci. 26, No. 4, 296-298 (2017). MSC: 11B68 11D45 PDFBibTeX XMLCite \textit{J. Bai} and \textit{X. Zhao}, J. Yunnan Minzu Univ., Nat. Sci. 26, No. 4, 296--298 (2017; Zbl 1399.11058) Full Text: DOI
Zhang, Yong; Shen, Zhongyan On the Diophantine system \(f(z)= f(x) f(y)= f(u) f(v)\). (English) Zbl 1387.11024 Period. Math. Hung. 75, No. 2, 295-301 (2017). Reviewer: Thomas Schmidt (Corvallis) MSC: 11D25 11D72 11G05 PDFBibTeX XMLCite \textit{Y. Zhang} and \textit{Z. Shen}, Period. Math. Hung. 75, No. 2, 295--301 (2017; Zbl 1387.11024) Full Text: DOI
He, Zongyou On the Diophantine equation \(y(y + 1)(y + 2)(y + 3) = n^2x(x + 1)(x + 2)(x + 3)\). (Chinese. English summary) Zbl 1389.11080 J. Yunnan Minzu Univ., Nat. Sci. 26, No. 2, 137-139, 143 (2017). MSC: 11D25 PDFBibTeX XMLCite \textit{Z. He}, J. Yunnan Minzu Univ., Nat. Sci. 26, No. 2, 137--139, 143 (2017; Zbl 1389.11080)
Pan, Xiaowei A note on the exponential Diophantine equation \((am^2+1)^x+(bm^2-1)^y=(cm)^z\). (English) Zbl 1425.11058 Colloq. Math. 149, No. 2, 265-273 (2017). MSC: 11D61 PDFBibTeX XMLCite \textit{X. Pan}, Colloq. Math. 149, No. 2, 265--273 (2017; Zbl 1425.11058) Full Text: DOI
Xu, Aijuan; Deng, Moujie On the Diophantine equation \(p^x + (p + 1)^y =z^2\). (Chinese. English summary) Zbl 1389.11090 J. Nat. Sci. Heilongjiang Univ. 33, No. 6, 766-769 (2016). MSC: 11D61 PDFBibTeX XMLCite \textit{A. Xu} and \textit{M. Deng}, J. Nat. Sci. Heilongjiang Univ. 33, No. 6, 766--769 (2016; Zbl 1389.11090) Full Text: DOI
Guan, Chunmei; Wu, Xingxing; Zhang, Sibao; Xi, Xiaozhong The positive integer solutions of Diophantine equation \(\varphi(xyz) = 5(\varphi(x) + \varphi(y) + \varphi(z))\). (Chinese. English summary) Zbl 1374.11005 J. Northwest Norm. Univ., Nat. Sci. 52, No. 4, 17-21 (2016). MSC: 11A25 PDFBibTeX XMLCite \textit{C. Guan} et al., J. Northwest Norm. Univ., Nat. Sci. 52, No. 4, 17--21 (2016; Zbl 1374.11005) Full Text: DOI
Wang, Rong; Liao, Qunying On the solvability of the equation \(\varphi_e(n) = \frac{n}{d}\) \((e = 1, 2, 4)\). (Chinese. English summary) Zbl 1374.11011 Pure Appl. Math. 32, No. 5, 481-494 (2016). MSC: 11A25 PDFBibTeX XMLCite \textit{R. Wang} and \textit{Q. Liao}, Pure Appl. Math. 32, No. 5, 481--494 (2016; Zbl 1374.11011) Full Text: DOI
Zhang, Xiaobeng; Li, Xiaoxue The number of solutions of the generalized Ramanujan-Nagell equation \(x^2+D^m=4p^n\). (Chinese. English summary) Zbl 1374.11059 J. Shaanxi Norm. Univ., Nat. Sci. Ed. 44, No. 4, 11-13 (2016). MSC: 11D61 11D45 PDFBibTeX XMLCite \textit{X. Zhang} and \textit{X. Li}, J. Shaanxi Norm. Univ., Nat. Sci. Ed. 44, No. 4, 11--13 (2016; Zbl 1374.11059) Full Text: DOI
Zhang, Zhengping; Zhao, Kaiming On the positive integer solutions of a class of generalized Ramanujan-Nagell equation. (Chinese. English summary) Zbl 1374.11046 J. Math., Wuhan Univ. 36, No. 5, 1077-1082 (2016). MSC: 11D09 11D45 PDFBibTeX XMLCite \textit{Z. Zhang} and \textit{K. Zhao}, J. Math., Wuhan Univ. 36, No. 5, 1077--1082 (2016; Zbl 1374.11046)
Zhang, Sibao Three kinds of equations involving Euler function. (Chinese. English summary) Zbl 1363.11033 Math. Pract. Theory 46, No. 8, 287-291 (2016). MSC: 11B68 11B83 PDFBibTeX XMLCite \textit{S. Zhang}, Math. Pract. Theory 46, No. 8, 287--291 (2016; Zbl 1363.11033)
Guan, Xungui On the Diophantine equation \(x^2-kxy+ y^2 + px = 0\). (Chinese. English summary) Zbl 1363.11050 Math. Pract. Theory 46, No. 8, 206-212 (2016). MSC: 11D09 PDFBibTeX XMLCite \textit{X. Guan}, Math. Pract. Theory 46, No. 8, 206--212 (2016; Zbl 1363.11050)
Du, Xiaoying Positive integer solutions of Mordell’s equation \(y^3 = x^2 + 2p^4\). (Chinese. English summary) Zbl 1363.11052 Math. Pract. Theory 46, No. 1, 263-266 (2016). MSC: 11D25 11D45 PDFBibTeX XMLCite \textit{X. Du}, Math. Pract. Theory 46, No. 1, 263--266 (2016; Zbl 1363.11052)
Hu, Jiayuan; Li, Xiaoxue All solutions of the Diophantine equation \(x^2 +2^m = y^n\). (Chinese. English summary) Zbl 1349.11075 Math. Pract. Theory 45, No. 24, 291-296 (2015). MSC: 11D61 PDFBibTeX XMLCite \textit{J. Hu} and \textit{X. Li}, Math. Pract. Theory 45, No. 24, 291--296 (2015; Zbl 1349.11075)
Guan, Xungui On the diophantine equation \(\frac{1}{x^2}+\frac{1}{y^2} =\frac{n}{z^2}\). (Chinese. English summary) Zbl 1349.11068 J. Ningxia Univ., Nat. Sci. Ed. 36, No. 4, 315-317, 321 (2015). MSC: 11D25 PDFBibTeX XMLCite \textit{X. Guan}, J. Ningxia Univ., Nat. Sci. Ed. 36, No. 4, 315--317, 321 (2015; Zbl 1349.11068)
Gao, Li; Ma, Yafeng An equation involving the Smarandache LCM dual function. (Chinese. English summary) Zbl 1349.11003 J. Hubei Univ., Nat. Sci. 37, No. 4, 367-371 (2015). MSC: 11A25 PDFBibTeX XMLCite \textit{L. Gao} and \textit{Y. Ma}, J. Hubei Univ., Nat. Sci. 37, No. 4, 367--371 (2015; Zbl 1349.11003) Full Text: DOI
Guan, Xungui On Terai’s conjecture concerning the Diophantine equation \(a^x +b^y= c^z\). (Chinese. English summary) Zbl 1349.11074 Adv. Math., Beijing 44, No. 6, 837-844 (2015). MSC: 11D61 PDFBibTeX XMLCite \textit{X. Guan}, Adv. Math., Beijing 44, No. 6, 837--844 (2015; Zbl 1349.11074) Full Text: DOI
Liu, Miaohua; Song, Xiuchao The necessary conditions for the equation \(x^3+1=3py^2\) having positive integer solutions. (Chinese. English summary) Zbl 1340.11034 J. Inn. Mong. Norm. Univ., Nat. Sci. 44, No. 1, 19-21 (2015). MSC: 11D25 PDFBibTeX XMLCite \textit{M. Liu} and \textit{X. Song}, J. Inn. Mong. Norm. Univ., Nat. Sci. 44, No. 1, 19--21 (2015; Zbl 1340.11034)
Wang, Jianping; Wang, Tingting; Zhang, Wenpeng A note on the exponential Diophantine equation \((4m^2+1)^x+(5m^2-1)^y=(3m)^z\). (English) Zbl 1364.11087 Colloq. Math. 139, No. 1, 121-126 (2015). MSC: 11D61 PDFBibTeX XMLCite \textit{J. Wang} et al., Colloq. Math. 139, No. 1, 121--126 (2015; Zbl 1364.11087) Full Text: DOI
Feng, Qiang; Han, Di On the Diophantine system \(a^2+b^2=c^r\) and \(a^x+b^y=c^z\) for \(b\) is a prime. (English) Zbl 1339.11047 Int. J. Appl. Math. Stat. 52, No. 7, 65-73 (2014). MSC: 11D61 PDFBibTeX XMLCite \textit{Q. Feng} and \textit{D. Han}, Int. J. Appl. Math. Stat. 52, No. 7, 65--73 (2014; Zbl 1339.11047) Full Text: Link
Wang, Jianhua; Wang, Xiaohan The upper bound for solutions of the generalized Brocard-Ramanujan equation \(x^2-D=y!\). (Chinese. English summary) Zbl 1324.11032 Basic Sci. J. Text. Univ. 27, No. 3, 290-292 (2014). MSC: 11D09 PDFBibTeX XMLCite \textit{J. Wang} and \textit{X. Wang}, Basic Sci. J. Text. Univ. 27, No. 3, 290--292 (2014; Zbl 1324.11032)
Guan, Wenji; Che, Shun On the Diophantine equation \(2^yn^{y-x}=(b+2)^x-b^x\). (Chinese. English summary) Zbl 1313.11072 J. Northwest Univ., Nat. Sci. Ed. 44, No. 4, 534-536 (2014). MSC: 11D61 PDFBibTeX XMLCite \textit{W. Guan} and \textit{S. Che}, J. Northwest Univ., Nat. Sci. Ed. 44, No. 4, 534--536 (2014; Zbl 1313.11072)
Liu, Baoli A note on the ternary pure exponential Diophantine equations. (Chinese. English summary) Zbl 1313.11073 J. Inn. Mong. Norm. Univ., Nat. Sci. 43, No. 4, 401-402, 407 (2014). MSC: 11D61 PDFBibTeX XMLCite \textit{B. Liu}, J. Inn. Mong. Norm. Univ., Nat. Sci. 43, No. 4, 401--402, 407 (2014; Zbl 1313.11073)
Zhu, Minhui; Zhang, Juanjuan; Cui, Yan The criteria for the equation \(x^3-1=2py^2\) having positive integer solutions. (Chinese. English summary) Zbl 1313.11064 J. Inn. Mong. Norm. Univ., Nat. Sci. 43, No. 4, 397-400 (2014). MSC: 11D25 PDFBibTeX XMLCite \textit{M. Zhu} et al., J. Inn. Mong. Norm. Univ., Nat. Sci. 43, No. 4, 397--400 (2014; Zbl 1313.11064)
Wang, Xiaohan On the Diophantine equation \(p^{2m}-Dx^2=1\). (Chinese. English summary) Zbl 1313.11074 Basic Sci. J. Text. Univ. 27, No. 1, 45-47 (2014). MSC: 11D61 PDFBibTeX XMLCite \textit{X. Wang}, Basic Sci. J. Text. Univ. 27, No. 1, 45--47 (2014; Zbl 1313.11074)
Su, Juanli The criteria for the equation \(x^3-8=py^2\) has primitive positive integer solutions. (Chinese. English summary) Zbl 1313.11061 Basic Sci. J. Text. Univ. 27, No. 1, 38-41 (2014). MSC: 11D25 PDFBibTeX XMLCite \textit{J. Su}, Basic Sci. J. Text. Univ. 27, No. 1, 38--41 (2014; Zbl 1313.11061)
Zheng, Hui On the Diophantine equation \(x(x+1)(x+2)=2p^ky^n\). (Chinese. English summary) Zbl 1313.11063 J. Southwest Univ. Natl., Nat. Sci. 40, No. 3, 399-401 (2014). MSC: 11D25 PDFBibTeX XMLCite \textit{H. Zheng}, J. Southwest Univ. Natl., Nat. Sci. 40, No. 3, 399--401 (2014; Zbl 1313.11063) Full Text: DOI
Du, Xiancun; Wan, Fei; Zhao, Jin’e On the Diophantine equation \(x^3\pm 1=pD_1y^2\). (Chinese. English summary) Zbl 1313.11059 J. Anhui Univ., Nat. Sci. 38, No. 2, 23-26 (2014). MSC: 11D25 PDFBibTeX XMLCite \textit{X. Du} et al., J. Anhui Univ., Nat. Sci. 38, No. 2, 23--26 (2014; Zbl 1313.11059) Full Text: DOI
Yang, Hai; Fu, Ruiqin A kind of an exponential Diophantine system and its integer solution. (Chinese. English summary) Zbl 1299.11036 J. Northwest Univ., Nat. Sci. Ed. 43, No. 4, 524-526 (2013). MSC: 11D61 PDFBibTeX XMLCite \textit{H. Yang} and \textit{R. Fu}, J. Northwest Univ., Nat. Sci. Ed. 43, No. 4, 524--526 (2013; Zbl 1299.11036)
Che, Shun An equation involving Smarandache function \(S(n)\) and pseudo Smarandache function \(Z_1(n)\) and its positive integer solutions. (Chinese. English summary) Zbl 1289.11003 Basic Sci. J. Text. Univ. 26, No. 1, 15-17 (2013). MSC: 11A25 PDFBibTeX XMLCite \textit{S. Che}, Basic Sci. J. Text. Univ. 26, No. 1, 15--17 (2013; Zbl 1289.11003)
Wu, Huaming On the cubic Diophantine equation \(x^3+1=3py^2\). (Chinese. English summary) Zbl 1274.11083 J. Northwest Univ., Nat. Sci. Ed. 43, No. 1, 15-17 (2013). MSC: 11D25 PDFBibTeX XMLCite \textit{H. Wu}, J. Northwest Univ., Nat. Sci. Ed. 43, No. 1, 15--17 (2013; Zbl 1274.11083)
Cheng, Zhi; Sun, Cuifang; Du, Xianneng On the Diophantine equation \((20n)^x+(21n)^y=(29n)^z\). (English) Zbl 1274.11088 Math. Appl. 26, No. 1, 129-133 (2013). MSC: 11D61 PDFBibTeX XMLCite \textit{Z. Cheng} et al., Math. Appl. 26, No. 1, 129--133 (2013; Zbl 1274.11088)
He, Bo; Togbé, Alain; Yang, Shichun On the solutions of the exponential Diophantine equation \(a^x+b^y=(m^2+1)^z\). (English) Zbl 1274.11086 Quaest. Math. 36, No. 1, 119-135 (2013). MSC: 11D41 11D09 11D61 PDFBibTeX XMLCite \textit{B. He} et al., Quaest. Math. 36, No. 1, 119--135 (2013; Zbl 1274.11086) Full Text: DOI
Liu, Yanyan An equation involving the L.C.M. product of the arithmetical function. (Chinese. English summary) Zbl 1274.11010 J. Inn. Mong. Norm. Univ., Nat. Sci. 41, No. 6, 601-603 (2012). MSC: 11A25 PDFBibTeX XMLCite \textit{Y. Liu}, J. Inn. Mong. Norm. Univ., Nat. Sci. 41, No. 6, 601--603 (2012; Zbl 1274.11010)
Ulas, Maciej Some observations on the Diophantine equation \(y^2=x!+A\) and related results. (English) Zbl 1291.11079 Bull. Aust. Math. Soc. 86, No. 3, 377-388 (2012). MSC: 11D85 11Y50 PDFBibTeX XMLCite \textit{M. Ulas}, Bull. Aust. Math. Soc. 86, No. 3, 377--388 (2012; Zbl 1291.11079) Full Text: DOI
Qian, Longjiang An equation involving the Smarandache function and the pseudo-Smarandache function of second kind. (Chinese. English summary) Zbl 1249.11043 Pure Appl. Math. 27, No. 5, 577-580 (2011). MSC: 11B83 PDFBibTeX XMLCite \textit{L. Qian}, Pure Appl. Math. 27, No. 5, 577--580 (2011; Zbl 1249.11043)
Wu, Huaming A rational fractional Diophantine equation. (English) Zbl 1240.11055 J. Math., Wuhan Univ. 31, No. 3, 428-432 (2011). MSC: 11D25 PDFBibTeX XMLCite \textit{H. Wu}, J. Math., Wuhan Univ. 31, No. 3, 428--432 (2011; Zbl 1240.11055)
Yuan, Xia Two equations involving the F. Smarandache function. (Chinese. English summary) Zbl 1240.11022 J. Inn. Mong. Norm. Univ., Nat. Sci. 40, No. 2, 129-131 (2011). MSC: 11A25 PDFBibTeX XMLCite \textit{X. Yuan}, J. Inn. Mong. Norm. Univ., Nat. Sci. 40, No. 2, 129--131 (2011; Zbl 1240.11022)
Le, Maohua A note on the Diophantine equation \( (a-1)x^2+f (a)=4a^n\). (Chinese. English summary) Zbl 1240.11061 Acta Math. Sin., Chin. Ser. 54, No. 1, 111-114 (2011). MSC: 11D61 PDFBibTeX XMLCite \textit{M. Le}, Acta Math. Sin., Chin. Ser. 54, No. 1, 111--114 (2011; Zbl 1240.11061)
Wu, Xin An equation involving the pseudo-Smarandache dual function. (Chinese. English summary) Zbl 1240.11020 J. Inn. Mong. Norm. Univ., Nat. Sci. 39, No. 6, 557-559 (2010). MSC: 11A25 PDFBibTeX XMLCite \textit{X. Wu}, J. Inn. Mong. Norm. Univ., Nat. Sci. 39, No. 6, 557--559 (2010; Zbl 1240.11020)
Li, Caijuan An equation involving two Smarandache functions and its positive integer solutions. (Chinese. English summary) Zbl 1240.11013 J. Nat. Sci. Heilongjiang Univ. 27, No. 4, 446-448, 454 (2010). MSC: 11A25 PDFBibTeX XMLCite \textit{C. Li}, J. Nat. Sci. Heilongjiang Univ. 27, No. 4, 446--448, 454 (2010; Zbl 1240.11013)
Gao, Jie; Yuan, Jin On the Diophantine equation \(x^3+1=py^2\). (Chinese. English summary) Zbl 1240.11052 Pure Appl. Math. 26, No. 4, 687-690 (2010). MSC: 11D25 PDFBibTeX XMLCite \textit{J. Gao} and \textit{J. Yuan}, Pure Appl. Math. 26, No. 4, 687--690 (2010; Zbl 1240.11052)
Yang, Shichun; Liao, Qunying A note of the solutions of Lebesgue-Nagell equation \(x^2+D=y^p\). (Chinese. English summary) Zbl 1240.11065 J. Sichuan Univ., Nat. Sci. Ed. 47, No. 4, 718-722 (2010). MSC: 11D61 11D45 PDFBibTeX XMLCite \textit{S. Yang} and \textit{Q. Liao}, J. Sichuan Univ., Nat. Sci. Ed. 47, No. 4, 718--722 (2010; Zbl 1240.11065) Full Text: DOI
He, Bo; Yang, Shichun The positive integer solution of Diophantine equations \((8a^3-3a)^x+(3a^2-1)^y=(4a^2-1)^z\). (Chinese. English summary) Zbl 1240.11058 J. Sichuan Univ., Nat. Sci. Ed. 47, No. 1, 13-16 (2010). MSC: 11D61 11D45 PDFBibTeX XMLCite \textit{B. He} and \textit{S. Yang}, J. Sichuan Univ., Nat. Sci. Ed. 47, No. 1, 13--16 (2010; Zbl 1240.11058) Full Text: DOI
Zhang, Jin An equation involving the pseudo Smarandache function and its dual function. (Chinese. English summary) Zbl 1224.11043 Pure Appl. Math. 25, No. 4, 786-788 (2009). MSC: 11B83 PDFBibTeX XMLCite \textit{J. Zhang}, Pure Appl. Math. 25, No. 4, 786--788 (2009; Zbl 1224.11043)
Wu, Zhaoxia; Wu, Nan A congruence equation involving the Smarandache function. (Chinese. English summary) Zbl 1212.11010 J. Northwest Univ., Nat. Sci. Ed. 39, No. 4, 549-551 (2009). MSC: 11A25 11A07 PDFBibTeX XMLCite \textit{Z. Wu} and \textit{N. Wu}, J. Northwest Univ., Nat. Sci. Ed. 39, No. 4, 549--551 (2009; Zbl 1212.11010)
Zhao, Yuane On a congruence equation of the Smarandache function. (Chinese. English summary) Zbl 1199.11003 Pure Appl. Math. 25, No. 1, 80-82 (2009). MSC: 11A07 PDFBibTeX XMLCite \textit{Y. Zhao}, Pure Appl. Math. 25, No. 1, 80--82 (2009; Zbl 1199.11003)
Li, Fanbei; Wang, Yuguang An equation involving the Euler function and the Smarandache \(m\)-th power residues function. (English) Zbl 1219.11005 Zhang, Wenpeng (ed.), Research on number theory and Smarandache notions. Proceedings of the fifth international conference on number theory and Smarandache notions, Shangluo, China, March 27–30, 2009. Phoenix, AZ: Hexis (ISBN 978-1-59973-088-2/pbk). 31-33 (2009). MSC: 11A25 PDFBibTeX XMLCite \textit{F. Li} and \textit{Y. Wang}, in: Research on number theory and Smarandache notions. Proceedings of the fifth international conference on number theory and Smarandache notions, Shangluo, China, March 27--30, 2009. Phoenix, AZ: Hexis. 31--33 (2009; Zbl 1219.11005)
Wang, Chunping; Zhao, Yanlin On an equation involving the Smarandache function and the Dirichlet divisor function. (English) Zbl 1219.11007 Zhang, Wenpeng (ed.), Research on number theory and Smarandache notions. Proceedings of the fifth international conference on number theory and Smarandache notions, Shangluo, China, March 27–30, 2009. Phoenix, AZ: Hexis (ISBN 978-1-59973-088-2/pbk). 27-30 (2009). MSC: 11A25 PDFBibTeX XMLCite \textit{C. Wang} and \textit{Y. Zhao}, in: Research on number theory and Smarandache notions. Proceedings of the fifth international conference on number theory and Smarandache notions, Shangluo, China, March 27--30, 2009. Phoenix, AZ: Hexis. 27--30 (2009; Zbl 1219.11007)
Li, Fanbei A functional equation related to the Smarandache function and its positive integer solutions. (Chinese. English summary) Zbl 1199.11012 J. Northwest Univ., Nat. Sci. Ed. 38, No. 6, 892-894 (2008). MSC: 11A25 PDFBibTeX XMLCite \textit{F. Li}, J. Northwest Univ., Nat. Sci. Ed. 38, No. 6, 892--894 (2008; Zbl 1199.11012)
Zhang, Wenpeng On two problems of the Smarandache function. (Chinese. English summary) Zbl 1199.11033 J. Northwest Univ., Nat. Sci. Ed. 38, No. 2, 173-176 (2008). MSC: 11A25 PDFBibTeX XMLCite \textit{W. Zhang}, J. Northwest Univ., Nat. Sci. Ed. 38, No. 2, 173--176 (2008; Zbl 1199.11033)
Zhu, Minhui An equation involving the Smarandache function and its positive integer solutions. (English) Zbl 1199.11036 Sci. Magna 4, No. 4, 1-3 (2008). MSC: 11A25 PDFBibTeX XMLCite \textit{M. Zhu}, Sci. Magna 4, No. 4, 1--3 (2008; Zbl 1199.11036)
Cheng, Bin On the pseudo Smarandache square-free function. (English) Zbl 1199.11006 Sci. Magna 4, No. 2, 21-24 (2008). MSC: 11A25 PDFBibTeX XMLCite \textit{B. Cheng}, Sci. Magna 4, No. 2, 21--24 (2008; Zbl 1199.11006)
Zhang, Pei An equation involving the pseudo-Smarandache squarefree function. (Chinese. English summary) Zbl 1199.11032 J. Zhengzhou Univ., Nat. Sci. Ed. 40, No. 2, 36-38 (2008). MSC: 11A25 PDFBibTeX XMLCite \textit{P. Zhang}, J. Zhengzhou Univ., Nat. Sci. Ed. 40, No. 2, 36--38 (2008; Zbl 1199.11032)