(a) For all a, b E Z, prove that a³b²-ab is even. (b) Let V = {0, 1, 2, 3, ..., 13}. Draw the graph G = (V, E) where {s,

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A For All A B E Z Prove That A B Ab Is Even B Let V 0 1 2 3 13 Draw The Graph G V E Where S 1 (45.95 KiB) Viewed 41 times

(a) For all a, b E Z, prove that a³b²-ab is even. (b) Let V = {0, 1, 2, 3, ..., 13}. Draw the graph G = (V, E) where {s, t} E E if and only if 7 | (st) or 7| (s+t). (c) Prove that in any set of four integers, there exists a pair a, b such that 14 | (a³b²-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?]