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prime of the year, n^2 +1 \equiv 0 mod p^{2007}

Source: KJMO 2007 p8

May 2, 2019
number theoryprimepositive integerdivisornumber theory proposed

Problem Statement

Prime pp is called Prime of the Year if there exists a positive integer nn such that n2+1≡0n^2+ 1 \equiv 0 (modp2007mod p^{2007}). Prove that there are infi nite number of Primes of the Year.
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