Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How do you solve for X?

  1. Oct 19, 2006 #1
    5x = 1 (mod 13)
    13x = 2 (mod 23)
    37x = 5 (mod 13)
     
  2. jcsd
  3. Oct 19, 2006 #2

    radou

    User Avatar
    Homework Helper

  4. Oct 19, 2006 #3

    0rthodontist

    User Avatar
    Science Advisor

    You could use the chinese remainder theorem if you can put it in the appropriate form. For example if you find some k such that 5k = 1 mod 13 (Euclid's algorithm), then the first equation is x = k (mod 13).
     
  5. Oct 19, 2006 #4
    i started with this
    5x-1=13y
    x=(13y+1)/5
    y=1
    x then =12/5
    is that correct?
    -------------------------------
    13x-2=23y
    x=(23y+2)/13
    y=0
    x then = 2/13?
    -------------------------------

    37x-5=13y
    x=(13y+5)/37
    y=1
    x then = 18/37

    is that right?
     
  6. Oct 20, 2006 #5
    i have created an excel and create a table like this
    x 3x module7
    1 3 3
    2 6 6
    3 9 2
    4 12 5
    5 15 1

    What should i do with this graph to do with 13x=2(mod23)
     
  7. Oct 20, 2006 #6

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    As has been said, use the Chinese remainder theorem (whcih is Euclid's algorithm but dressed up).

    Of course if you typed it correctly you're looking for 5x=1 (13) and 37x=5 (13). Are those even compatible? The fact that you've written 37 and not 11 means that either you've mistyped the 13, or you're not happy with modulo arithmetic, and don't see that you can always replace something with something else congruent mod m if it helps.
     
  8. Oct 20, 2006 #7

    CRGreathouse

    User Avatar
    Science Advisor
    Homework Helper

    Nope, [itex]5\not\equiv8\pmod{13}[/itex].
     
  9. Oct 20, 2006 #8

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    Yes, I know. It was rhetorical/supposed to make the OP think about it, not someone for whom the question is easy.
     
  10. Oct 21, 2006 #9
    the answer to 5x = 1 (mod 13) is x = 8 (mod 13)
    and the answer to 13x = 2 (mod 23) is x = 9 (mod 23)
    and the answer to 37x = 5 (mod 13) is x = 4 (mod 13)
     
  11. Oct 22, 2006 #10

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    So those aren't sumultaneous equations then? It would greatly benefit you (and would stop you driving your teachers mad) if you wrote things unambiguously, and in full sentences.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Similar Discussions: How do you solve for X?
  1. How Do i Solve For X? (Replies: 5)

Loading...