(a) For all x, y e Z+, prove that x3y - xy3 is even. (b) Let V...

Question:

(a) For all x, y e Z+, prove that x3y - xy3 is even.
(b) Let V = {1,2,3,...,8, 9}. Construct the loop-free undirected graph G = (V, E) as follows: For m, n e V, m ≠ n, draw the edge [m, n] in G if 5 divides m + n or m - n.
(c) Given any three distinct positive integers, prove that there are two of these, say x and y, where 10 divides x3y - xy3.