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Number of roots of f(x)-n

Source: Kürschák 2004, problem 2

July 13, 2014
algebrapolynomialalgebra unsolved

Problem Statement

Find the smallest positive integer n≠2004n\neq 2004 for which there exists a polynomial f∈Z[x]f\in\mathbb{Z}[x] such that the equation f(x)=2004f(x)=2004 has at least one, and the equation f(x)=nf(x)=n has at least 20042004 different integer solutions.
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