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n divides 2^m+m

Source: IMO Shortlist 2006, N7, AIMO 2007, TST 7, P3

June 19, 2007
modular arithmeticnumber theoryDivisibilityexponentialIMO Shortlist

Problem Statement

For all positive integers nn, show that there exists a positive integer mm such that nn divides 2m+m2^{m} + m.
Proposed by Juhan Aru, Estonia
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