Problem

Source: SMO 2015 open

Tags: number theory, Fibonacci sequence



Let f0,f1,... be the Fibonacci sequence: f0=f1=1,fn=fn1+fn2 if n2. Determine all possible positive integers n so that there is a positive integer a such that fnafn+1 and that a(1f1+1f1f2++1f1f2...fn) is an integer.