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looks like euler, but it's not :)

Source: Romanian IMO Team Selection Test TST 2004, problem 13

May 24, 2004
Eulermodular arithmeticinequalitiesfunctionIMO Shortlistnumber theoryrelatively prime

Problem Statement

Let m≥2m\geq 2 be an integer. A positive integer nn has the property that for any positive integer aa coprime with nn, we have am−1≡0(modn)a^m - 1\equiv 0 \pmod n.
Prove that n≤4m(2m−1)n \leq 4m(2^m-1).
Created by Harazi, modified by Marian Andronache.
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