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a^{2^n}+2^n is not prime

Source: 239MO 2004, grade 8-9 and 10-11, problem 3

December 11, 2004
number theory unsolvednumber theory

Problem Statement

Prove that for any integer aa there exist infinitely many positive integers nn such that a2n+2na^{2^n}+2^n is not a prime. proposed by S. Berlov
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