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polynomial has exactly $n$ integral roots?

Source: All-Russian 2007

May 4, 2007
algebrapolynomialcalculusintegrationquadraticsalgebra proposed

Problem Statement

Do there exist non-zero reals aa, bb, cc such that, for any n>3n>3, there exists a polynomial Pn(x)=xn+⋯+ax2+bx+cP_{n}(x) = x^{n}+\dots+a x^{2}+bx+c, which has exactly nn (not necessary distinct) integral roots? N. Agakhanov, I. Bogdanov
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