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Polynomial - f(x)=1979 four times - prove f(x) not= 2*1979

Source: ILL 1979 - Problem 72.

June 5, 2011

algebrapolynomialcalculusintegrationalgebra unsolved

Problem Statement

Let

f (x)

be a polynomial with integer coefficients. Prove that if

f (x)= 1979

for four different integer values of

x

, then

f (x)

cannot be equal to

2\times 1979

for any integral value of

x