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(p^2 + p) (q^2 + q) (r^2 + r) perfect square for p,q,r primes

Source: Czech-Polish-Slovak Junior Match 2017, Team p1 CPSJ

March 6, 2020
perfect cubenumber theoryprimes

Problem Statement

Decide if there are primes p,q,rp, q, r such that (p2+p)(q2+q)(r2+r)(p^2 + p) (q^2 + q) (r^2 + r) is a square of an integer.
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