On a conjecture Mordell

Abstract

A conjecture of Mordell states that if $p$ is a prime and $p$ is congruent to $3$ mod $4$, then $p$ does not divide $y$ where $(x,y)$ is the fundamental solution to $x^2-p{y}^2=1$. The conjecture has been verified for primes not exceeding $10^7$. In this article, we show that Mordell's conjecture holds for four conjecturally infinite families of primes.

arXiv comment11 pages