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1 + P(x) = 1/2 (P(x -1) + P(x + 1))

Source: 2003 Swedish Mathematical Competition p4

March 21, 2021
algebrapolynomial

Problem Statement

Determine all polynomials PP with real coeffients such that 1+P(x)=12(P(x−1)+P(x+1))1 + P(x) = \frac12 (P(x -1) + P(x + 1)) for all real xx.
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