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Polynomial with Integer Coefficients

Source:

November 13, 2005
algebrapolynomialquadraticsVietafunctionAMCAIME

Problem Statement

Let P(x)P(x) be a polynomial with integer coefficients that satisfies P(17)=10P(17)=10 and P(24)=17P(24)=17. Given that P(n)=n+3P(n)=n+3 has two distinct integer solutions n1n_1 and n2n_2, find the product n1⋅n2n_1\cdot n_2.
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