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0163 Fibonacci 1st edition Round 6 p3

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May 9, 2021
number theory1st edition

Problem Statement

Consider (fn)n≥0(f_n)_{n\ge 0} the Fibonacci sequence, defined by f0=0f_0 = 0, f1=1f_1 = 1, fn+1=fn+fn−1f_{n+1} = f_n + f_{n-1} for all positive integers nn. Solve the following equation in positive integers nfnfn+1=(fn+2−1)2.nf_nf_{n+1} = (f_{n+2} - 1)^2. .
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