1. Find all polynomials $P(x)=a x^{2}+b x+c$ with integer coefficients satisfying

$$
1<P(1)<P(2)<P(3) \quad \text { and at the same time } \quad \frac{P(1) \cdot P(2) \cdot P(3)}{4}=17^{2} \text {. }
$$