Translator Disclaimer
2019 On a conjecture of Mordell
Debopam Chakraborty, Anupam Saikia
Rocky Mountain J. Math. 49(8): 2545-2556 (2019). DOI: 10.1216/RMJ-2019-49-8-2545

Abstract

A conjecture of Mordell states that if $p$ is a prime and $p$ is congruent to $3$ modulo $4$, then $p$ does not divide $y$ where $(x,y)$ is the fundamental solution to $x^{2}-py^{2}=1$. 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.

Citation

Download Citation

Debopam Chakraborty. Anupam Saikia. "On a conjecture of Mordell." Rocky Mountain J. Math. 49 (8) 2545 - 2556, 2019. https://doi.org/10.1216/RMJ-2019-49-8-2545

Information

Published: 2019
First available in Project Euclid: 31 January 2020

zbMATH: 07163185
MathSciNet: MR4058336
Digital Object Identifier: 10.1216/RMJ-2019-49-8-2545

Subjects:
Primary: 11A55, 11D09
Secondary: 11R11, 11R27

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
12 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.49 • No. 8 • 2019
Back to Top