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Find k where n doesn't divide greatest odd divisor of k^n+1

Source: XVII Olimpíada Matemática Rioplatense (2008)

July 25, 2011
number theory unsolvednumber theory

Problem Statement

Find all integers k≥2k\ge 2 such that for all integers n≥2n\ge 2, nn does not divide the greatest odd divisor of kn+1k^n+1.
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