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Math Help - Solving Modulars

  1. #1
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    Solving Modulars

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    251^1001 (mod 101)
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  2. #2
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    Quote Originally Posted by dylanx5 View Post
    Need Help with this
    251^1001 (mod 101)
    251^{1001}=(251^{100})^{10}251^1 but according Fermat's theorem 251^{100} in Z_{101} is 1^{100} so you have that 251^{1001} in Z_{101} is 251\bmod 101 =49
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  3. #3
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    thanks a lot
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  4. #4
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    Quote Originally Posted by andreas View Post
    251^{1001}=(251^{100})^{10}251^1 but according Fermat's theorem 251^{100} in Z_{101} is 1^{100} so you have that 251^{1001} in Z_{101} is 251\bmod 101 =49

    what does this symbol mean though ( Z_{101}) in literal terms. is it to base 101??
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  5. #5
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    it means set of integers from +-(0 to 100). Another words all possible remainders after division by 101
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