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Math Help - need help with these congruence and other problems for number theory

  1. #1
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    need help with these congruence and other problems for number theory

    1) If k > 2, and n = 2k-3, show that 3n is not congruent to 1 (mod 2k).
    2) Let p > 3 be a prime, and suppose that p 3 (mod 4). If q = 2p+1 is also prime show that 2p -1 is never prime.
    3) Let p be a prime 2 or 5, and let N be any integer. If p | (N2-5) show that p is of the form 1+5k, or 4+5k
    4) Let p be a prime. Show that every prime divisor of 2p -1 is > p.
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    Re: need help with these congruence and other problems for number theory

    Quote Originally Posted by henderson7878 View Post
    1) If k > 2, and n = 2k-3, show that 3n is not congruent to 1 (mod 2k).
    2) Let p > 3 be a prime, and suppose that p 3 (mod 4). If q = 2p+1 is also prime show that 2p -1 is never prime.
    3) Let p be a prime 2 or 5, and let N be any integer. If p | (N2-5) show that p is of the form 1+5k, or 4+5k
    4) Let p be a prime. Show that every prime divisor of 2p -1 is > p.
    And what have you been able to do so far?

    And for the sake of clarity, please do not post so many questions in one thread.

    -Dan
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