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Prove that if o is the m -cycle(12 ... m). Show that o' is also an m cycle iff i is relatively prime to m.

Prove that if o is the m -cycle(12 ... m). Show that o' is also an m cycle iff i is relatively prime to m.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I need some assistance proving this modern algebra question. She said use induction but I dunno where start.

10. Prove that if \( \sigma \) is the \( m \)-cycle \( (1\ 2\ \ldots\ m) \), show that \( \sigma^i \) is also an \( m \)-cycle if and only if \( i \) is relatively prime to \( m \).
Transcribed Image Text:10. Prove that if \( \sigma \) is the \( m \)-cycle \( (1\ 2\ \ldots\ m) \), show that \( \sigma^i \) is also an \( m \)-cycle if and only if \( i \) is relatively prime to \( m \).
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