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(Well known?) polynomial

Source: 2023 Serbia TST Problem 4

May 22, 2023
algebrapolynomialSerbiaTST

Problem Statement

Let pp be a prime and P∈R[x]P\in \mathbb{R}[x] be a polynomial of degree less than p−1p-1 such that ∣P(1)∣=∣P(2)∣=…=∣P(p)∣\lvert P(1)\rvert=\lvert P(2)\rvert=\ldots=\lvert P(p)\rvert. Prove that PP is constant.
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