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Equation Equivalence

  1. Jun 20, 2012 #1
    1. The problem statement, all variables and given/known data
    Show that:

    7x≈3 mod(15)


    2. Relevant equations
    From the given above I think it should be:

    7x-3=15n

    3. The attempt at a solution
    I tried factoring this in various ways to show that either said was a factor of the other, but I'm struggling here.

    But I don't know what to do from here. I actually have several of these problems, but I assume that once I know how to do the first one, they will be easy.

    Thoughts? Thanks!
    James
     
  2. jcsd
  3. Jun 20, 2012 #2

    Curious3141

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    Homework Helper

    Well, for starters, it isn't true in general (for all x).

    counterexample: for x = 3, 7*3 = 21 = 6 mod 15
     
  4. Jun 20, 2012 #3

    Mark44

    Staff: Mentor

    So, since the equation isn't generally true, maybe the aim of the problem was to find the values of x for which it is true.
     
  5. Jun 21, 2012 #4

    Curious3141

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    Homework Helper

    In which case "Show that:", etc. is a terrible phrasing for it.
     
  6. Jun 21, 2012 #5

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Yes, it is!

    Hammonjj, you want to solve 7x= 3 (mod 15) for x. Of course, that is the same as x= (3/7) (mod 15) so you really just want to know how to write 3/7 in this mod 15 system.

    Notice that 7(2)= 14= -1 (mod 15) so that 7(-2)= 1 (mod 15). And, since 15- 2= 13, 1/7= -2= 13 (mod 15). Now, what is 3/7 (mod 15)?
     
  7. Jun 21, 2012 #6
    Always verify with 0
     
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