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- 21. (a) Prove that if d | n, then 2d -1 | 2″ – 1. [Hint: Use the identity k-2 x − 1 = (x − 1)(x*−1 + x*-² + ··· +x+1).]

- 21. (a) Prove that if d | n, then 2d -1 | 2″ – 1. [Hint: Use the identity k-2 x − 1 = (x − 1)(x*−1 + x*-² + ··· +x+1).]

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 5E: 5. Prove that the equation has no solution in an ordered integral domain.
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- 21. (a) Prove that if d | n, then 2d -1 | 2″ – 1. [Hint: Use the identity k-2 x − 1 = (x − 1)(x*−1 + x*-² + ··· +x+1).]
Transcribed Image Text:- 21. (a) Prove that if d | n, then 2d -1 | 2″ – 1. [Hint: Use the identity k-2 x − 1 = (x − 1)(x*−1 + x*-² + ··· +x+1).]
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