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Fibonacci powers

Source: 2012 Indonesia Round 2 TST 3 Problem 4

March 18, 2012
number theory unsolvednumber theory

Problem Statement

The Fibonacci sequence {Fn}\{F_n\} is defined by F1=F2=1F_1 = F_2 = 1 and Fn+2=Fn+1+FnF_{n+2} = F_{n+1} + F_n for all positive integers nn. Determine all triplets of positive integers (k,m,n)(k,m,n) such that Fn=FmkF_n = F_m^k.
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