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IMO ShortList 2001, number theory problem 4

Source: IMO ShortList 2001, number theory problem 4

September 30, 2004
number theoryIMO Shortlist

Problem Statement

Let p≥5p \geq 5 be a prime number. Prove that there exists an integer aa with 1≤a≤p−21 \leq a \leq p-2 such that neither ap−1−1a^{p-1}-1 nor (a+1)p−1−1(a+1)^{p-1}-1 is divisible by p2p^2.
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