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What is the smallest positive integer n such that x^n - 1 is factored into precisely five irreducible factors?

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What is the smallest positive integer n such that x^n - 1 is factored into precisely five irreducible factors?
posted Nov 26, 2017 by anonymous

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1 Answer

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n=16

Explanation

x^16 - 1
= (x^8+1)(x^8-1)
= (x^8+1)(x^4+1)(x^4-1)
= (x^8+1)(x^4+1)(x^2+1)(x^2-1)
= (x^8+1)(x^4+1)(x^2+1)(x-1)(x+1)

answer Dec 31, 2017 by Yasin Hossain Siinan
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