MathDB
Beautiful polynomial number theory

Source: Baltic Way 2004 Problem 8, "extended" and "generalized"

November 20, 2004
algebrapolynomialinequalitiesfunctionlogarithmsnumber theoryprime numbers

Problem Statement

Let f(x)f\left(x\right) be a non-constant polynomial with integer coefficients, and let uu be an arbitrary positive integer. Prove that there is an integer nn such that f(n)f\left(n\right) has at least uu distinct prime factors and f(n)≠0f\left(n\right) \neq 0.
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