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Fermat-like nondivisibility

Source: Mongolian MO 2002 Teachers P4

April 9, 2021
number theory

Problem Statement

Let p≥5p\ge5 be a prime number. Prove that there exists a∈{1,2,…,p−2}a\in\{1,2,\ldots,p-2\} satisfying p2∤ap−1−1p^2\nmid a^{p-1}-1 and p2∤(a+1)p−1−1p^2\nmid(a+1)^{p-1}-1.
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