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Math Help - modulo and congruence classes

  1. #1
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    modulo and congruence classes

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    Last edited by yellow4321; March 6th 2008 at 06:28 AM.
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  2. #2
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    Quote Originally Posted by yellow4321 View Post
    how could i use fermats little theorem on 5^72(mod73) provided my calculator cannot have output of greater than 200. if i used say (5^8)^9 (mod72) id be here forever.

    start of like 5^72 congruent to 1 mod 73 ??i guess

    2.) how would i calculate the inverse of [5] (subscript/base 27) in Z/27 (Z-intergers)

    id want to end up with 1mod27 i think just need help getting there.
    Are you asking for a proof of Fermat's little theorem?
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  3. #3
    Senior Member JaneBennet's Avatar
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    Quote Originally Posted by yellow4321 View Post
    2.) how would i calculate the inverse of [5] (subscript/base 27) in Z/27 (Z-intergers)

    id want to end up with 1mod27 i think just need help getting there.
    You want to find an integer n such that 5n leaves a remainder 1 when divided by 27. Well, 5 times any integer ends in 0 or 5. So just find a multiple of 27 that ends in 4 or 9, and add 1 to it. 27 2 = 54; 54 + 1 = 55 = 5 11. So the multiplicative inverse of 5 in \mathbb{Z}_{27} is 11.
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