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Composite Fibonacci Terms

Problem

Let $F_n$ represents the $n^{th}$ term of the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, ... .

Prove that for all composite values of $n \gt 4, F_n$ is composite.

Problem ID: 365 (03 Nov 2009)     Difficulty: 4 Star

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