MathDB

13

Part of 2004 Romania Team Selection Test

Problems(1)

looks like euler, but it's not :)

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

5/24/2004
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.
Eulermodular arithmeticinequalitiesfunctionIMO Shortlistnumber theoryrelatively prime