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!

Number theory LMC and GCF equation.

  1. May 7, 2012 #1
    1. The problem statement, all variables and given/known data

    (E) : 2Lcm(x,y)-5gcf(x,y0=7

    2. Relevant equations

    1- Find the possible values of the the number T=gcf(x,y)

    2- Solve in N^2 the equation (E).

    3. The attempt at a solution

    For number 1 i transformed the equation and I found an equivalence of 2T Ξ 7(mod 5gcf(x,y) is that correct, and how can i proceed.
     
    Last edited: May 7, 2012
  2. jcsd
  3. May 7, 2012 #2

    I like Serena

    User Avatar
    Homework Helper

    That would not be correct.
    It seems you mixed up T and Lcm.

    It would be correct that:
    5T Ξ -7(mod 2Lcm(x,y))
    and also that:
    5T Ξ -7(mod 2)
    5T Ξ -7(mod Lcm(x,y))

    As an extra observation, which number would have to divide the left hand side and therefore also the right hand side?
     
  4. May 7, 2012 #3
    Is that number 1?
     
  5. May 7, 2012 #4

    I like Serena

    User Avatar
    Homework Helper

    Of course 1, but there is also another number.
    More importantly, what do Lcm and Gcf have in common?
     
  6. May 7, 2012 #5
    LCM*GCF=x*y

    and if we make into a form of an equation we get that 5t+7=lcm(x,y)*k where k is a n integer.
     
  7. May 7, 2012 #6

    I like Serena

    User Avatar
    Homework Helper

    Yes.
    Can you say more?

    Hmm, that is not true.
    Where did the "2" go?
     
  8. May 7, 2012 #7



    Yes: gcd(x,y) divides lcm(x,y) Right???
     
  9. May 7, 2012 #8

    I like Serena

    User Avatar
    Homework Helper

    Yep. So...
     
  10. May 7, 2012 #9
    So 2 divides 5T? I'm not quite sure can you help me a little bit more?
     
  11. May 7, 2012 #10

    I like Serena

    User Avatar
    Homework Helper

    Uhh... no... that is not true either. :confused:

    Does T divide the left hand side?
     
  12. May 7, 2012 #11
    yes it does so i'm guessing it has to divide -7+2klcm(x,y) right??
     
  13. May 7, 2012 #12

    I like Serena

    User Avatar
    Homework Helper

    Uhh... yes...?
     
  14. May 7, 2012 #13
    So... how can i find the values of T then??
     
  15. May 7, 2012 #14
    So the Values of T are those that divide lcm(x,y)??
     
  16. May 7, 2012 #15
    So...
    Does gcd(x,y) divide 2*lcm(x,y)?
    Does gcd(x,y) divide 5*gcd(x,y)?
    Does gcd(x,y) divide 2*lcm(x,y) - 5*gcd(x,y)?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Number theory LMC and GCF equation.
Loading...