1. Limited time only! Sign up for a free 30min personal 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!

Co-prime of vectors

  1. Feb 7, 2012 #1
    Hi guys

    I have a question about the coprime of two vectors
    For two vectors (x1,x2) and (y1,y2).
    Given a,b with gcf (a,b)=1 .i.e. relatively prime.
    I do the linear combination of two vectors
    a(x1,x2)+b(y1,y2)=n(z1,z2) with some common factor n and gcf(z1,z2)=1.
    If n=1 for any a,b, two vectors are said co-prime.
    I wonder if any criteria to prove two vectors are coprime.
    For example, (2,3),(1,3) are not coprime b/c (2,3)+(1,3)=3(1,2).
    But (7,3),(2,1) are coprime b/c a(7,3)+b(2,1)=(7a+2b,3a+b) and gcf(7a+2b,3a+b)=gcf(a,3a+b)=gcf(a,b)=1.
    Also how to generalize it to vectors with n components?

    Thank you
     
  2. jcsd
  3. Feb 8, 2012 #2
    I don't know if there's a name for this operation.
    But I can recommend that you move the thread to the Number Theory forum, it seems to belong there more.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook