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Math Help - Units Mod N

  1. #1
    Junior Member mathmonster's Avatar
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    Units Mod N

    ive got the answer to this question, but it took a lot of time and was very tedious. i just want to know if there is a nice quick solution so when i hand in the worksheet it doesnt look a mess.

    the question is

    calculate 17^-1 in Z43 (integers mod 43)

    i just did multiplication tables for both and found when 43r -17s = 1 but its not a really 'nice' method. thanks for ur time
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  2. #2
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    Quote Originally Posted by mathmonster View Post
    ive got the answer to this question, but it took a lot of time and was very tedious. i just want to know if there is a nice quick solution so when i hand in the worksheet it doesnt look a mess.

    the question is

    calculate 17^-1 in Z43 (integers mod 43)

    i just did multiplication tables for both and found when 43r -17s = 1 but its not a really 'nice' method. thanks for ur time
    We want to find 17x - 43 y = 1 for integers x,y.

    Use Euclidean algorithm,
    43 = 2\cdot 17 + 9
    17 = 1\cdot 9 + 8
    9 = 1\cdot 8 + 1

    Working backwards,
    1 = 9- 8 = 9 - (17 - 9) = 2\cdot 9 - 17 = 2(43 - 2\cdot 17) - 17 = 2\cdot 43 - 5\cdot 17

    Thus, the inverse is  - 5\equiv 38.
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