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Quartic polynomial prime divisors

Source: XIII Ibero American Olympiad For University Students

July 22, 2011
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Problem Statement

Prove that, for all integer a>1a>1, the prime divisors of 5a4−5a2+15a^4-5a^2+1 have the form 20k±1,k∈Z20k\pm1,k\in\mathbb{Z}.
Proposed by Géza Kós.
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