A polynomial $P(x,y)$ with integer coefficients satisfies two following conditions: 1. for every integer $a$ there exists exactly one integer $y$, such that $P(a,y)=0$ 2. for every integer $b$ there exists exactly one integer $x$, such that $P(x,b)=0$ a) Prove that if the degree of $P$ is $2$, then it is divisible by either $x-y+C$ for some integer $C$, or $x+y+C$ for some integer $C$ b) Is there a polynomial $P$ that isn't divisible by any of $x-y+C$ or $x+y+C$ for integers $C$?