Part 4. Prove the following mathematical statements. Let n be any integer. a. If n – 1 is odd, then n² is even. b. If n² is even, then n is also even. c. Not all prime numbers are odd. (Hint: Proof by existence)
Part 4. Prove the following mathematical statements. Let n be any integer. a. If n – 1 is odd, then n² is even. b. If n² is even, then n is also even. c. Not all prime numbers are odd. (Hint: Proof by existence)
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.2: Mathematical Induction
Problem 1E: Prove that the statements in Exercises are true for every positive integer .
1.
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