2007 USAMO Problems/Problem 5
The proof is by induction. The base is provided by the case, where . To prove the inductive step, it suffices to show that if for some positive integer then is composite. As a consequence, has at least two more prime factors than does . To confirm that is composite, observe that Also each factor exceeds 1. It suffices to check the smaller one; gives Hence is composite and the proof is complete.
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