Discrete Mathematics

Q3 (14 points) (a) For all a, b e Z, prove that a3b2 - abt is even. . (b) Let V = {0,1,2,3,...,13). Draw the graph G=(V, E) where {s,t} Eif and only if 7 (s t) or 7(s+t). Prove that in any set of four integers, there exists a pair a, b such that 14| (ab? ab4). [Hint: Factor the expression. Consider integers modulo n, which n would be relevant? What information can be gathered from the connected components of the above graph?]