On the Diophantine equation X^2N + 2^{2 alpha} 5^{2 beta} p^{2 gamma} = Z⁵

2014/09/08 by Eva G. Goedhart, Goedhart, Eva G., Helen G. Grundman +1
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Advanced Mathematical Theories and Applications #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.1409.2463

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} = Z⁵ has no solution with X, Z, N in Z⁺, N > 1, and gcd(X,Z) = 1.

Related

• A note on the Diophantine equations x²±5^α⋅ pⁿ=yⁿ
• On the Diophantine Equation p^x + p^y = z²ⁿ
• On the Diophantine Equation x²+5^a⋅ 11^b=yⁿ
• A refined modular approach to the Diophantine equation x²+y²ⁿ=z³
• A generalization of the Ramanujan-Nagell equation