Problem

Source: X International Festival of Young Mathematicians Sozopol 2019, Theme for 10-12 grade

Tags: number theory, prime numbers, modulo



Let $p_1, p_2, p_3$, and $p$ be prime numbers. Prove that there exist $x,y\in \mathbb{Z}$ such that $y^2\equiv p_1 x^4-p_1 p_2^2 p_3^2\, (mod\, p)$.