MathDB

p(x) does not take the value 8 for any integer x [easy one]

Source: IMO LongList 1970 - P48

November 9, 2010

algebrapolynomialalgebra proposed

Problem Statement

Let a polynomial

p(x)

with integer coefficients take the value

5

for five different integer values of

x.

Prove that

p(x)

does not take the value

8

for any integer

x.