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Precalculus Mathematics Homework Help
Proof about cycle with odd length
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[QUOTE="fishturtle1, post: 5888585, member: 606256"] [h2]Homework Statement [/h2] In the following problems let ##\alpha## be a cycle of length ##s##, and say ##\alpha = (a_1a_2 . . . a_s)##. 5) If ##s## is odd, ##\alpha## is the square of some cycle of length s. (Find it. Hint: Show ##\alpha = \alpha^{s+1}##) [h2]Homework Equations[/h2][h2]The Attempt at a Solution[/h2] I know ##(12345)(12345) = (12345)## and ##(1234)(1234) = (13)(24)##. And I think I can prove this is true for any integer n, such that if a cycle ##\alpha## has an odd length, then squaring it produces another cycle of odd length, and ##\alpha## has an even length, s, then its square is the product of two disjoint cycles, each of length s/2. I guess I've pretty much restated the problem... I'm stuck. For the hint.. I know ##\alpha## of length ##s## has ##\alpha## distinct powers but I'm not sure how to prove it. Sorry this is so bare bones, thank you for any help [/QUOTE]
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Precalculus Mathematics Homework Help
Proof about cycle with odd length
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