If x n </msup> is irrational for some n &#x2208; N , how do I prove that

opepayflarpws

opepayflarpws

Answered question

2022-06-26

If x n is irrational for some n N, how do I prove that x d is irrational for any divisor d of n?

Answer & Explanation

Jayce Bates

Jayce Bates

Beginner2022-06-27Added 18 answers

Suppose x d is rational. Then ( ( x d ) c = x d c = x n (where d c = n, since d n) must also be rational, which is a contradiction. Thus x d is irrational.

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