Determine the greatest common divisor GCD (xn-1,Xm-1) where m, n are nonzero natural numbers. Please write the complete solution with steps.

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter6: Fractions
Section6.4: Least Common Denominators
Problem 13E
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Determine the greatest common divisor GCD (xn-1,Xm-1) where m, n are nonzero natural numbers.

Please write the complete solution with steps.

Hint: Use Euclid's algorithm for m,n respectively f and g or with roots of unity any method is acceptable or maybe you have other ideas.

Thanks in advance

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