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Thread: Finding inverses

  1. July 9th 2011, 02:20 PM #1
    scruz10
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    Finding inverses

    Just wondering if there was a method to find inverses besides just guess and check. I need to find for Z/365Z the inverses of [53], [73], [93], and [113]
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  2. July 9th 2011, 06:38 PM #2
    hatsoff
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    Re: Finding inverses

    Quote Originally Posted by scruz10 View Post
    Just wondering if there was a method to find inverses besides just guess and check. I need to find for Z/365Z the inverses of [53], [73], [93], and [113]
    Under addition we the have -[53]=[-53], and so on. Multiplication is a bit trickier. Use the Euclidean algorithm to find a,b such that 53a+365b=1. Then [53]^{-1}=[a]. However keep in mind that [73] is NOT an element of the multiplicative group Z/365Z (because (73,365)=73).
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