Mordell's conjecture on Pell equation solutions for primes congruent to 3 modulo 4

Let $p$ be a prime congruent to $3$ modulo $4$, and let $(x,y)$ be a fundamental solution of the Pell equation

$$x^2-py^2=1.$$

Mordell's conjecture. The prime $p$ does not divide $y$.

This conjecture concerns divisibility properties of the fundamental solution to Pell equations associated with primes congruent to $3$ modulo $4$. It was proved by Chakraborty, so the conjecture is solved.