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Integers in Boxes

Source: OMM 2009 2

July 15, 2014
inductionmodular arithmeticnumber theory unsolvednumber theory

Problem Statement

In boxes labeled 00, 11, 22, …\dots, we place integers according to the following rules:
∙\bullet If pp is a prime number, we place it in box 11.
∙\bullet If aa is placed in box mam_a and bb is placed in box mbm_b, then abab is placed in the box labeled amb+bmaam_b+bm_a.
Find all positive integers nn that are placed in the box labeled nn.
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