(a) $k(k-1)a_{k,l} + l(l-1)a_{k-2,l} = 0$ for $2 \le k, l \le n$; \newline (b) $a_{n-1,l} = a_{n,l} = 0$ for $2 \le l \le n$; \newline (c) $a_{k,n-1} = a_{k,n} = 0$ for $2 \le k \le n$. \newline 4. Prove that a nonconstant harmonic function on a region is an open map. \newline (Hint: Use the fact that the connected subsets of R are intervals.)
