Question 19
Let $S=\{(a, b) \mid a, b=1,2,3,4$, and $a \neq b\}$, and consider all nonzero polynomials $p(X, Y)$ with integer coefficients such that $p(a, b)=0$ for every element $(a, b)$ in $S$.
(a) What is the minimal degree of such polynomial $p(X, Y)$?
(b) Determine all such polynomials $p(X, Y)$ with minimal degree.
(a) What is the minimal degree of such polynomial $p(X, Y)$?
(b) Determine all such polynomials $p(X, Y)$ with minimal degree.