order of a cycle example 1

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Find the order of a cycle. Reference to Hohn Fraleigh Text: A Frirst Course In Abstract Algebra. Note at the end e=(1)(2)(3)(4)(5)(6)(7)(8)
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Depends on order of p. If p has order 4, then divides 2011 by 4, remainder is 3 as 2011=4(502)+3. then p^2011 = p^3

S
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i have been asked to find p^2011

How do I do that?

Thanks again!

BB