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Coefficients of Gamma function

Source: China TST 2000, problem 4

May 22, 2005
functionalgebrapolynomialalgebra unsolved

Problem Statement

Let FF be the set of all polynomials Γ\Gamma such that all the coefficients of Γ(x)\Gamma (x) are integers and Γ(x)=1\Gamma (x) = 1 has integer roots. Given a positive intger kk, find the smallest integer m(k)>1m(k) > 1 such that there exist Γ∈F\Gamma \in F for which Γ(x)=m(k)\Gamma (x) = m(k) has exactly kk distinct integer roots.
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