Tell me how to do this proof.

It's hard...

Oh, you must know group theory and symmetry groups in order to attempt this.

Let sigma = (1 2 3 ... n) be in S_n (a cycle) with n>=1. Let k be a positive integer.

Show that if k is relatively prime to n, then sigma^k (with the operation being composition, obviously) is a cycle, that is, sigma applied k times can be written as one cycle of length greater than one composed with possibly a bunch of disjoint cycles of length 1.

Any ideas?

Um, could you put that into LaTeX and post an image of the equation? The wording is really confusing.

Quote:

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Originally Posted by ninja9578

Um, could you put that into LaTeX and post an image of the equation? The wording is really confusing.

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There's no equation...words are just words.

The only thing even remotely resembling as equation is (1 2 ... n ) e S_n, where e is actually "is an element of". But the notation (1 2 ... n ) is cycle notation and is exactly how I wrote it.