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one of a^n+1, a^{n+1}+1 , ... , a^{2n-2}+1 does not have a common divisor

Source: Rioplatense Olympiad 2012 level 3 P5

September 4, 2018
number theorydivisor

Problem Statement

Let a≥2a \ge 2 and n≥3n \ge 3 be integers . Prove that one of the numbers an+1,an+1+1,...,a2n−2+1a^n+ 1 , a^{n + 1}+ 1 , ... , a^{2 n-2}+ 1 does not share any odd divisor greater than 11 with any of the other numbers.
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