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Prove that d >= p-1

Source: IMO Shortlist 1997, Q12

August 26, 2005
algebrapolynomialmodular arithmeticcongruenceIMO Shortlist

Problem Statement

Let p p be a prime number and f f an integer polynomial of degree d d such that f(0)=0,f(1)=1 f(0) = 0,f(1) = 1 and f(n) f(n) is congruent to 0 0 or 1 1 modulo p p for every integer n n. Prove that d≥p−1 d\geq p - 1.
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