On the Diophantine equation x^4-q^4=py^5

Details On the Diophantine equation x^4-q^4=py^5 On the Diophantine equation x^4-q^4=py^5

2009-07-03

arxiv.org/abs/0907.0692v1

Mathematics

Number Theory

This paper was accepted for publication in Italian Journal of Pure and Applied Mathematics

Scientific paper

In this paper we study the Diophantine equation $x^{4}-q^{4}=py^{5},$ with
the following conditions: $p$ and $q$ are different prime natural numbers, $y$
is not divisible with $p$, $p\equiv3$ (mod20), $q\equiv4$ (mod5),
$\overline{p}$ is a generator of the group $(U(\textbf{Z}_{q^{4}}),\cdot)$,
$(x,y)=1$, 2 is a 5-power residue mod $q$.

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