title: On the system of Diophantine equations x2 - 6y2 = -5 and x = az2 - b.
abstract: Mignotte and Pethö used the Siegel-Baker method to find all the integral solutions (x, y, z) of the system of Diophantine equations x (2) - 6y (2) = -5 and x = 2z (2) - 1. In this paper, we extend this result and put forward a generalized method which can completely solve the family of systems of Diophantine equations x (2) - 6y (2) = -5 and x = az (2) - b for each pair of integral parameters a, b. The proof utilizes algebraic number theory and p-adic analysis which successfully avoid discussing the class number and factoring the ideals.
authors.affiliation: School of Mathematics and Statistics, Wuhan University, Hubei 430072, China ; College of Science, Huazhong Agricultural University, Hubei 430070, China.
authors.forename: Silan
authors.initials: S
authors.lastname: Zhang
authors.affiliation: School of Mathematics and Statistics, Wuhan University, Hubei 430072, China.
authors.forename: Jianhua
authors.initials: J
authors.lastname: Chen
authors.affiliation: School of Mathematics and Statistics, Wuhan University, Hubei 430072, China.
authors.forename: Hao
authors.initials: H
authors.lastname: Hu
mesh_terms: D008962:Models, Theoretical