Solutions to the Diophantine Equation p3x = z2 − 17 for Odd Primes p

EasyChair Preprint 14054

Abstract

In this paper, we investigate the solutions to the Diophantine equation
p3x = z2 − 17,
where p is a fixed odd prime, and x and z are positive integers. We examine
specific cases and provide a detailed analysis of the solutions. Notably,
one solution is given by (p, x, z) = (2, 1, 5). This study contributes to the
broader understanding of the behavior of such equations and their integer
solutions.

Keyphrases: Prime number, integer, odd prime

@booklet{EasyChair:14054,
  author    = {Budee U Zaman},
  title     = {Solutions to the Diophantine Equation p3x = z2 − 17 for Odd Primes p},
  howpublished = {EasyChair Preprint 14054},
  year      = {EasyChair, 2024}}