If $p,p^2+2$ are both primes, how many divisors does $p^5+2p^2$ have? (Zhuge Liang)
Problem
Source: Mathcenter Contest / Oly - Thai Forum 2012 sl-3 https://artofproblemsolving.com/community/c3196914_mathcenter_contest
Tags: number theory, divisible, primes