Problem

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2016 Shortlist N1 day2

Tags: number theory, Diophantine equation, diophantine



Let $p> 5$ be a prime such that none of its digits is divisible by $3$ or $7$. Prove that the equation $x^4 + p = 3y^4$ does not have integer solutions.