On a conjecture Mordell

2018/10/14 by Chakraborty, Debopam, Saikia, Anupam
#11A55 #11D09 #11R11 #11R27 #11R29 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1810.05980

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 x²-py²=1. The conjecture has been verified for primes not exceeding 10⁷. In this article, we show that Mordell's conjecture holds for four conjecturally infinite families of primes.

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