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Existence of infinitely many a for which n^4+a is composite

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September 29, 2010
number theorySophie Germain identitycomposite numbersIMO ShortlistIMO Longlist

Problem Statement

(GDR2)IMO1(GDR 2)^{IMO1} Prove that there exist infinitely many natural numbers aa with the following property: The number z=n4+az = n^4 + a is not prime for any natural number n.n.
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