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10. Let m and n are two positive integers with m > n. Let a be a positive integer. Prove that a2" +1 is a divisor of a2 1. Also, prove that (a2" + 1, a" + 1) = 1 if a is even and (a2" + 1, a2" + 1) = 2 if a is odd.

10. Let m and n are two positive integers with m > n. Let a be a positive integer. Prove that a2" +1 is a divisor of a2 1. Also, prove that (a2" + 1, a" + 1) = 1 if a is even and (a2" + 1, a2" + 1) = 2 if a is odd.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.4: Prime Factors And Greatest Common Divisor
Problem 28E: Let and be positive integers. If and is the least common multiple of and , prove that . Note...
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10. Let m and n are two positive integers with m > n. Let a be a positive integer. Prove that a +1 is a divisor of a2 - 1. Also, prove that (a2" + 1, a2" + 1) = 1 if a is even and (a2" +1, a2" + 1) = 2 if a is odd.
Transcribed Image Text:10. Let m and n are two positive integers with m > n. Let a be a positive integer. Prove that a +1 is a divisor of a2 - 1. Also, prove that (a2" + 1, a2" + 1) = 1 if a is even and (a2" +1, a2" + 1) = 2 if a is odd.
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