Let P(x) be a polynomial with integer coefficients that satisfies P(17)=10 and P(24)=17. Given that the equation P(n)=n+3 has two distinct integer solutions n_{1} and n_{2}, find the product n_{1} \cdot n_{2}.
Let P(x) be a polynomial with integer coefficients that satisfies P(17)=10 and P(24)=17. Given that the equation P(n)=n+3 has two distinct integer solutions n_{1} and n_{2}, find the product n_{1} \cdot n_{2}.