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no of divisors of (p^5+2p^2) if p,p^2+2 are both primes

Source: Mathcenter Contest / Oly - Thai Forum 2012 sl-3 https://artofproblemsolving.com/community/c3196914_mathcenter_contest

November 13, 2022
number theorydivisibleprimes

Problem Statement

If p,p2+2p,p^2+2 are both primes, how many divisors does p5+2p2p^5+2p^2 have?
(Zhuge Liang)
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