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Math Help - Modular Exponentiation

  1. #1
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    Modular Exponentiation

    Hello,

    I can't recall how to deal with large exponents in modular arithmetic.

    Specifically, the question is to determine the value of 8^402 mod 5.

    It is equivalent to (2^402 mod 5)^3 (since 2^3=8) from what I recall, but not sure how that helps...

    Thanks!
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  2. #2
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    Quote Originally Posted by matt.qmar View Post
    Hello,

    I can't recall how to deal with large exponents in modular arithmetic.

    Specifically, the question is to determine the value of 8^402 mod 5.

    It is equivalent to (2^402 mod 5)^3 (since 2^3=8) from what I recall, but not sure how that helps...

    Thanks!
    Here because 5 is prime we can use Fermat's Little Theorem and in general we can use Euler's theorem (which requires gcd of the base and the modulus to be 1).

    So it's 8^{402}\equiv 3^{2}\equiv 4\pmod{5}.
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