N3

Part of 2013 IMO Shortlist

Problems(1)

IMO Shortlist 2013, Number Theory #3

Source: IMO Shortlist 2013, Number Theory #3

Prove that there exist infinitely many positive integers

n

such that the largest prime divisor of

n^4 + n^2 + 1

is equal to the largest prime divisor of

(n+1)^4 + (n+1)^2 +1

number theoryprime divisorpolynomialIMO Shortlistimo shortlist n3Hi