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Find All k

Source: Czech and Slovak Match 1999

July 28, 2006
algebrapolynomialalgebra proposed

Problem Statement

Find all positive integers kk for which the following assertion holds: If F(x)F(x) is polynomial with integer coefficients ehich satisfies F(c)≤kF(c) \leq k for all c∈{0,1,⋯ ,k+1}c \in \{0,1, \cdots,k+1 \}, then F(0)=F(1)=⋯=F(k+1).F(0)= F(1) = \cdots =F(k+1).
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