2005 AIME II Problem 13

Let P(x) be a polynomial with integer coefficients that satisfies P(17)=10 and P(24)=17. Given that P(n)=n+3 has two distinct integer solutions n_1 and n_2, find the product n_1\cdot n_2.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.