2012 IMO Shortlist N8

Prove that for every prime $p>100$ and every integer $r$ there exist two integers $a$ and $b$ such that $p$ divides $a^{2}+b^{5}-r$.

证明对于每个素数 $p>100$ 和每个整数 $r$，存在两个整数 $a$ 和 $b$，使得 $p$ 整除 $a^{2}+b^{5}-r$。