Answered: For any n > 1, prove that the…

For any n > 1, prove that the irreducible factorization over Z ofxn-1 + xn-2 + . . . +x +1 is π Φd (x), where the product runs overall positive divisors d of n greater than 1.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.4: Zeros Of A Polynomial

Problem 34E

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For any n > 1, prove that the irreducible factorization over Z of
x^n-1 + x^n-2 + . . . +x +1 is π Φ_d (x), where the product runs over
all positive divisors d of n greater than 1.

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