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3. Prove that if n is odd, then 8 divides n2- 1. Prove that 6 divides n п. 4. Let n and k be two positive integers with n 2. Prove that (n-1)² divides n-1 if and only if n-1 divides k.

3. Prove that if n is odd, then 8 divides n2- 1. Prove that 6 divides n п. 4. Let n and k be two positive integers with n 2. Prove that (n-1)² divides n-1 if and only if n-1 divides k.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.2: Mathematical Induction
Problem 7E
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3. Prove that if n is odd, then 8 divides n2 – 1. Prove that 6 divides n3 - п. | 4. Let n and k be two positive integers with n > 2. Prove that (n - 1)² divides nk -1 if and only if n - 1 divides k.
Transcribed Image Text:3. Prove that if n is odd, then 8 divides n2 – 1. Prove that 6 divides n3 - п. | 4. Let n and k be two positive integers with n > 2. Prove that (n - 1)² divides nk -1 if and only if n - 1 divides k.
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