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Math Help - Least Residue!

  1. #1
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    Least Residue!

    Can someone pls help me with this question????

    Find the least residue of 789^3217 modulo the prime 1607.
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  2. #2
    Super Member PaulRS's Avatar
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    Remember Fermat's Little Theorem, if p is prime and a a natural number then a^p\equiv{a}(\bmod.{p})

    For our case: 789^{1607}\equiv{789}(\bmod.{1607})

    Squaring: 789^{3214}\equiv{789^2}(\bmod.{1607})

    And: 789^{3217}\equiv{789^5}\equiv{772}(\bmod.{1607})
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  3. #3
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    How did you get the 789^5?

    HEy Thanks!

    I'm just not sure how you got the 789^5.
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