1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Diophantine Equations/GCD

  1. Mar 13, 2008 #1
    1. The problem statement, all variables and given/known data
    Suppose that gcd(a,b)=1 and that a|n and b|n. Prove that ab|n.


    2. Relevant equations
    Since we know that gcd(a,b)=1, we can say that ax+by=1 for some x,y as elements of the integer set.


    3. The attempt at a solution
    My professor said I should multiply the entire equation by n, but I still can't figure it out. Any help would be appreciated. Thanks in advance.
     
  2. jcsd
  3. Mar 14, 2008 #2
    I also have another problem that takes priority over this one if anybody can help.

    Prove that (2n)!/(2^n*n!) is an odd number when n is a nonnegative integer.
     
  4. Mar 14, 2008 #3

    morphism

    User Avatar
    Science Advisor
    Homework Helper

    If you multiply the equation by n, you get n=nax+nby. Now use the fact that both a & b divide n.

    For your second problem, have you tried expanding (2n)!/(2^n*n!) out?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Diophantine Equations/GCD
  1. Diophantine Equations (Replies: 2)

  2. Diophantine Equation (Replies: 1)

  3. Diophantine equation (Replies: 0)

  4. Diophantine equation (Replies: 1)

Loading...