MathDB

Non-constant polynomials with integer coefficients

Source: IMO Longlist 1989, Problem 51

September 18, 2008

algebrapolynomialalgebra unsolved

Problem Statement

Let f(x) \equal{} \prod^n_{k\equal{}1} (x \minus{} a_k) \minus{} 2, where

n \geq 3

and

a_1, a_2, \ldots,

an are distinct integers. Suppose that f(x) \equal{} g(x)h(x), where

g(x), h(x)

are both nonconstant polynomials with integer coefficients. Prove that n \equal{} 3.