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Proceedings of the American Mathematical Society

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The Diophantine equation $ x\sp 2=4q\sp n+4q\sp m+1$


Author: Mao Hua Le
Journal: Proc. Amer. Math. Soc. 106 (1989), 599-604
MSC: Primary 11D61
DOI: https://doi.org/10.1090/S0002-9939-1989-0968624-6
MathSciNet review: 968624
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Abstract: Let $ q = {p^r}$ be a prime power. In this paper, we prove that the equation $ {x^2} = 4{q^n} + 4{q^m} + 1,m < n,{\text{g}}{\text{.c}}{\text{.d}}{\text{.}}(m,n) = 1$ has no positive integer solution $ (m,n,x)$ with $ m > 2$.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0968624-6
Article copyright: © Copyright 1989 American Mathematical Society