On the Diophantine equation x⁴-q⁴=py⁵

2009/07/03 by Diana Savin, Savin, Diana
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Advanced Mathematical Theories and Applications #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.0907.0692

Abstract

In this paper we study the Diophantine equation x⁴-q⁴=py⁵, with the following conditions: p and q are different prime natural numbers, y is not divisible with p, p≡3 (mod20), q≡4 (mod5), p is a generator of the group (U(Z_q⁴),⋅), (x,y)=1, 2 is a 5-power residue mod q.

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