2

Part of 2004 Kurschak Competition

Problems(1)

Number of roots of f(x)-n

Source: Kürschák 2004, problem 2

Find the smallest positive integer

n\neq 2004

for which there exists a polynomial

f\in\mathbb{Z}[x]

such that the equation

f(x)=2004

has at least one, and the equation

f(x)=n

2004

different integer solutions.

algebrapolynomialalgebra unsolved