On the Diophantine equation X^{2N} + 2^{2 alpha} 5^{2 beta} p^{2 gamma} = Z^5

Eva G. Goedhart; Helen G. Grundman

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arXiv · 1409.2463

On the Diophantine equation X^{2N} + 2^{2 alpha} 5^{2 beta} p^{2 gamma} = Z^5

Eva G. Goedhart·Helen G. Grundman

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Abstract

We prove that for each odd prime p, positive integer alpha, and non-negative integers beta and gamma, the Diophantine equation X^{2N} + 2^{2 alpha} 5^{2 beta} p^{2 gamma} = Z^5 has no solution with X, Z, N in Z^+, N > 1, and gcd(X,Z) = 1.

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Eva G. Goedhart, Helen G. Grundman. 2014-09-08. On the Diophantine equation X^{2N} + 2^{2 alpha} 5^{2 beta} p^{2 gamma} = Z^5. https://arxiv.org/abs/1409.2463

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