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Math Help - Modular arithmetic

  1. #1
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    Yerevan
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    Modular arithmetic

    Please help my, Thanks

    Carefully explain you answers!

    (1) Let n = 3^(t-1). Show that 2^n = -1 (mod 3^t). (Hint: 2 is a primitive root mod 3^2.)



    (2) a) Let n be an integer >1, and suppose that p = 2^n+1 is a prime. Show that 3^((p-1)/2) +1

    is divisible by p. (Hint: First show that n must be even.)


    b) If p = 2^n+1, n>1, and 3^((p-1)/2) = -1 (mod p) show that p is a prime.



    (3)If n is positive integer what is the number of solutions (x,y) (with x and y positive

    integers) to the equation

    1/x + 1/y = 1/n .


    Carefully explain your reasoning.



    (5) Let p be a prime. Show that every prime divisor of 2^p -1 is > p.
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  2. #2
    Super Member PaulRS's Avatar
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    See here, here and here

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  3. #3
    Newbie
    Joined
    Dec 2008
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    Yerevan
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    thank you

    thank you very much, for Your halp.

    It's not for me (I'm astronomer).
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