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Math Help - modular calculation

  1. #1
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    modular calculation

    can anyone help me with this?

    calculate 45^41 mod13

    i know i'm probably meant to use fermat's little theorem but i can't see where..

    thanks!
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  2. #2
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    Quote Originally Posted by MariaJJ View Post
    can anyone help me with this?

    calculate 45^41 mod13

    i know i'm probably meant to use fermat's little theorem but i can't see where..

    thanks!

    45\equiv 6\,(mod\,13)\Longrightarrow 45^{41}=6^{41}=\left(6^{13}\right)^3\cdot 6^2=6^3\cdot 6^2=\left(6^2\right)^2\cdot 6=10^2\cdot 6=2\,\,(mod\,\,13)

    Tonio
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  3. #3
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    Quote Originally Posted by tonio View Post
    45\equiv 6\,(mod\,13)\Longrightarrow 45^{41}=6^{41}=\left(6^{13}\right)^3\cdot 6^2=6^3\cdot 6^2=\left(6^2\right)^2\cdot 6=10^2\cdot 6=2\,\,(mod\,\,13)

    Tonio
    @Tonio-If you can confirm (a yes/no would be sufficient plz)
    <br />
\left(6^{13}\right)^3\cdot 6^2=6^3\cdot 6^2

    This came from Fermat't little thoerm = a^p \equiv a mod p
    Correct?
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  4. #4
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    Quote Originally Posted by aman_cc View Post
    @Tonio-If you can confirm (a yes/no would be sufficient plz)
    <br />
\left(6^{13}\right)^3\cdot 6^2=6^3\cdot 6^2

    This came from Fermat't little thoerm = a^p \equiv a mod p
    Correct?

    Yes ssssir!

    Tonio
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