Problem

Source: China Zhejiang Fuyang , 27 Jul 2014

Tags: modular arithmetic, number theory unsolved, number theory



Let $p$ be a primes ,$x,y,z $ be positive integers such that $x<y<z<p$ and $\{\frac{x^3}{p}\}=\{\frac{y^3}{p}\}=\{\frac{z^3}{p}\}$. Prove that $(x+y+z)|(x^5+y^5+z^5).$