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Homework Help: Fermat's little theorem Question - exam in 2 days pls

  1. Aug 9, 2011 #1
    Dear sir/madam
    I have tried to do this question but can not figure it out. I gave up, but google gave me physicsforums site. I am very greatful and thanks for being genorous.

    question is attached

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    Last edited: Aug 9, 2011
  2. jcsd
  3. Aug 9, 2011 #2
    What did you try already?? If you tell us where you're stuck, then we'll know how to help...
  4. Aug 10, 2011 #3
    Sir, I really can not see any connection between this problem and FLT ..Pls give me some insight how to start out .. got 1day left :)
  5. Aug 10, 2011 #4
    We know [itex] n^{13} \equiv n \ ( mod \ 13)[/itex], right? That's the theorem.

    But we also know that if [itex] a' \equiv a \ ( mod \ m )[/itex] and [itex] b' \equiv b \ ( mod \ m )[/itex], then [itex] a'b' \equiv ab \ ( mod \ m )[/itex]. This implies

    [tex] n^{39} \equiv n^3 \ (mod \ 13).[/tex]

    But then what's another way to express this congruence? To say that [itex]n^{39}[/itex] is congruent to [itex]n^3[/itex] means 13 divides what?
  6. Aug 12, 2011 #5

    Dear Sir, Thanks very much for your time. Anyway FLT was not in the exam.. I had to do 4 questions but i did 6 questions... Well I passed it..Yehiiiiiiiiiiiiiiiiiiiiii

    I am truely greatful
    with metta
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