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 $$n_1\cdot n_2.$$

(第二十三届AIME2 2005 第13题)