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find all functions satisfying p | f(f(x)) − x^2

Source: STEMS 2024, CAT B, P5

December 17, 2023
functionalgebra

Problem Statement

Find the sum of all primes p<50p < 50, for which there exists a function f ⁣:{0,…,p−1}→{0,…,p−1}f \colon \{0, \ldots , p -1\} \rightarrow \{0, \ldots , p -1\} such that p∣f(f(x))−x2p \mid f(f(x)) - x^2.
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