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continous function f: [0,d] to R

Source: Problem 4, Polish NO 1988

October 16, 2005
functionalgebra unsolvedalgebra

Problem Statement

dd is a positive integer and f:[0,d]→Rf : [0,d] \rightarrow \mathbb{R} is a continuous function with f(0)=f(d)f(0) = f(d). Show that there exists x∈[0,d−1]x \in [0,d-1] such that f(x)=f(x+1)f(x) = f(x+1).
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