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

Diana Savin

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

Number Theory 2009-07-06 v1

Authors: Diana Savin

Abstract

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 $q$ .

Keywords

diophantine equations

Cite

@article{arxiv.0907.0692,
  title  = {On the Diophantine equation x^4-q^4=py^5},
  author = {Diana Savin},
  journal= {arXiv preprint arXiv:0907.0692},
  year   = {2009}
}

Comments

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

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