IMO 2008 Shortlist N3
Let a0,a1,a2,... be a sequence of positive integers such that the greatest common divisor of any two consecutive terms i...
Category: Number Theory
Problem
Let a0,a1,a2,... be a sequence of positive integers such that the greatest common divisor of any two consecutive terms is greater than the preceding term; in symbols, gcd(ai,ai+1) > ai−1. Prove that an ≥ 2n for all n ≥ 0.