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MMO 077 Moscow MO 1941 integer P(x), with odd values at 0,1, no integer roots

Source:

July 18, 2019

integer rootsInteger Polynomialpolynomialalgebra

Problem Statement

A polynomial

P(x)

with integer coefficients takes odd values at

x = 0

and

x = 1

. Prove that

P(x)

has no integer roots.