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Quick question regarding Fermat

  1. Mar 3, 2005 #1
    I have a question regarding mods and Fermat's Little Theorem. I know Fermat's little theorem states that a^p-1 congruent to 1 (mod p). Also, i know that for every interger a we have that a^p congruent to a (mod p). So, my question is: What is the answer for 3^302 (mod 5)? Would it be 3^301 congruent 1 (mod 5)? I am having a bit of difficulty understanding this concept. Any help?
     
    Last edited: Mar 3, 2005
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  3. Mar 3, 2005 #2

    Hurkyl

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    Well, Fermat's little theorem says 3^(5-1) = 1 (mod 5)...
     
  4. Mar 3, 2005 #3

    Zurtex

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    Consider 300 = 4*75 = (5-1)*75. So:

    So 3^(302) mod 5 = 3*3*[3^(300)] mod 5 = 3*3*[(3^75)^(5 - 1)] mod 5 = 3*3*1 mod 5

    I think you can do the rest :wink:
     
  5. Mar 3, 2005 #4
    thank you thank you all. by using this i can figure out the other five problems.
     
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