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IMO Shortlist 2013, Number Theory #3

Source: IMO Shortlist 2013, Number Theory #3

July 10, 2014
number theoryprime divisorpolynomialIMO Shortlistimo shortlist n3Hi

Problem Statement

Prove that there exist infinitely many positive integers nn such that the largest prime divisor of n4+n2+1n^4 + n^2 + 1 is equal to the largest prime divisor of (n+1)4+(n+1)2+1(n+1)^4 + (n+1)^2 +1.
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