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
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
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