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Slipping integers

Source: Centroamerican 2011, Problem 3

June 22, 2011
inequalitiesnumber theory proposednumber theory

Problem Statement

A slip on an integer n≥2n\geq 2 is an operation that consists in choosing a prime divisor pp of nn and replacing nn by n+p2p.\frac{n+p^2}{p}.
Starting with an arbitrary integer n≥5n\geq 5, we successively apply the slip operation on it. Show that one eventually reaches 55, no matter the slips applied.
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