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Lower bounds for the solutions in the second case of Fermat's last theorem


Author: Mao Hua Le
Journal: Proc. Amer. Math. Soc. 111 (1991), 921-923
MSC: Primary 11D41
DOI: https://doi.org/10.1090/S0002-9939-1991-1049137-1
MathSciNet review: 1049137
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Abstract: Let $ p$ be an odd prime. In this paper, we prove that if $ p \equiv 3$ and $ x,y,z$ are integers satisfying $ {x^p} + {y^p} = {z^p},p\vert xyz,0 < x < y < z$, then $ y > {2^{ - 1/p}}{p^{6p - 2}}$ and $ z - x > \tfrac{1}{2}{p^{6p - 3}}$.


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DOI: https://doi.org/10.1090/S0002-9939-1991-1049137-1
Article copyright: © Copyright 1991 American Mathematical Society

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