Find all primes $1 < p < 100$ such that the equation $x^2-6y^2=p$ has an integer solution $(x, y)$.
Source: 2014 Thailand October Camp Number Theory Quiz p1
Tags: number theory, prime numbers
Find all primes $1 < p < 100$ such that the equation $x^2-6y^2=p$ has an integer solution $(x, y)$.