Q3 (a) For all a, be Z prove that a b - ab4 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 | (s – t) or 7| (s+t). (C) Prove that in any set of four integers, there exists a pair a, b such that 14 | (a*b – 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?]
Q3 (a) For all a, be Z prove that a b - ab4 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 | (s – t) or 7| (s+t). (C) Prove that in any set of four integers, there exists a pair a, b such that 14 | (a*b – 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?]
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 48E
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