Results 1 to 2 of 2

Math Help - Help with some Proofs

  1. #1
    Member
    Joined
    Mar 2009
    Posts
    168

    Help with some Proofs

    I came across these theorems, I was wondering if anyone could help with them!

    1. Let a, b, n be elements of N with n >= 1. Prove that a and b are relatively prime iff a^n and b are relatively prime.

    2. Suppose a, b, c are elements of N with at least one not zero. How would you define the greatest common divisor of a, b, c? Prove that it exists AND is unique.

    I'm pretty sure for the 2nd one that gcd(a, b, c) = gcd(gcd(a,b), c). Any help actually PROVING these?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Mar 2009
    Posts
    168
    For the second one, I can prove the uniqueness easily. But proving the existence is more difficult to me.

    I want to prove that there exists a gcd of just a,b because then I could extend that out easily to gcd(gcd(a,b), c).

    So now I just need to know how can I prove that there exists a gcd of a and b?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. proofs
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: March 2nd 2010, 04:54 AM
  2. lim sup and lim inf proofs
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: February 24th 2010, 08:02 PM
  3. More Proofs
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: February 13th 2008, 08:05 PM
  4. Proofs
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 3rd 2008, 05:23 AM
  5. Replies: 3
    Last Post: October 6th 2007, 03:01 PM

Search Tags


/mathhelpforum @mathhelpforum