MathDB
Polynomial And Degrees

Source:

December 9, 2010
algebrapolynomialnumber theory unsolvednumber theory

Problem Statement

Let pp be a prime and Q(x)Q(x) be a polynomial with integer coefficients such that Q(0)=0, Q(1)=1Q(0) = 0, \ Q(1) = 1 and the remainder of Q(n)Q(n) is either 00 or 11 when divided by pp, for every n∈Nn \in \mathbb{N}. Prove that Q(x)Q(x) is of degree at least p−1p - 1.
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