11. Prove that for each integer a, if a² – 1 is even, then 4 divides a² – 1.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.2: Mathematical Induction
Problem 49E: Show that if the statement is assumed to be true for , then it can be proved to be true for . Is...
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Please answer 11

* 10. Is the following proposition true or false? Justify your conclusion.
For each integer n, n is even if and only if 4 divides n².
11. Prove that for each integer a, if a² – 1 is even, then 4 divides a? – 1.
Transcribed Image Text:* 10. Is the following proposition true or false? Justify your conclusion. For each integer n, n is even if and only if 4 divides n². 11. Prove that for each integer a, if a² – 1 is even, then 4 divides a? – 1.
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