Show that if $x^d -1$ divides $x^n -1$ if and only if $d$ divides $n$

Asked Sep 12 '19 at 15:19

Active Sep 13 '19 at 03:10

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I have done one part. If $d$ divides $n$ then $n=dp$ for some $p$ in $\mathbb{Z}$. Then $x^n -1=x^{dp} -1$. Then $x^d -1$ is a factor of $x^n-1$. So $x^d -1$ divides $x^n -1$.

But how to show reverse part?

edited Sep 12 '19 at 16:14

asked Sep 12 '19 at 15:19

Prince10572

8

This has been asked and answered here lots and lots of times, e.g. Prove：$x^d-1 \mid x^n-1$ iff $d \mid n$. – xxxxxxxxx Sep 12 '19 at 15:23

Show that if $x^d -1$ divides $x^n -1$ if and only if $d$ divides $n$

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