8. Prove the following statements: (a) If n is an even integer, then n2 - 6 is even. (b) If m is an odd integer, then m3 – 2m + 2 is odd.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.2: Properties Of Group Elements
Problem 31E: 31. Prove statement of Theorem : for all integers and .
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8. Prove the following statements:
(a) If n is an even integer, then n2 – 6 is even.
-
(b) If m is an odd integer, then m3 – 2m + 2 is odd.
Transcribed Image Text:8. Prove the following statements: (a) If n is an even integer, then n2 – 6 is even. - (b) If m is an odd integer, then m3 – 2m + 2 is odd.
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