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P(n) = n^3 -n^2 -5n+ 2 is a prime

Source: Austrian Mathematical Olympiad 2003, Part 2, D1, P1

June 18, 2011
algebrapolynomialnumber theory proposednumber theory

Problem Statement

Consider the polynomial P(n)=n3−n2−5n+2P(n) = n^3 -n^2 -5n+ 2. Determine all integers nn for which P(n)2P(n)^2 is a square of a prime.
[hide="Remark."]I'm not sure if the statement of this problem is correct, because if P(n)2P(n)^2 be a square of a prime, then P(n)P(n) should be that prime, and I don't think the problem means that.
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