Solve B (a) For all x, y = Z, prove that x¹y - x²y³ is even.(b) Let V = {0, 1, 2, 3,..., 13}. Draw the graph G = (V, E)where {s, t} € E if and only if 7 | (st) or 7| (s+t).(c) Prove that in any set of four integers, there exists a pair x, ysuch that 14 | (x4y - x²y³).[Hint: Factor the expression. Consider integers modulo n, whichn would be relevant? What information can be gathered fromthe connected components of the above graph?]

The vertex set is: V=0, 1, 2, 3, …, 13 The graph G=V, E has the property that s, t∈E if and only if…

Answered: (b) Let V = {0, 1, 2, 3,..., 13}. Draw…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 74EQ

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(b) Let V = {0, 1, 2, 3,..., 13}. Draw the graph G = (V, E) where {s, t} € E if and only if 7 | (s – t) or 7| (s+t).