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Equation question

  1. Nov 20, 2008 #1
    find a general solution and the number of solutions in Z5 field
    of this equation:

    X+Y-Z=1




    i know i need to
    y=0 z=1
    y=1 z=0
    but what next?
     
  2. jcsd
  3. Nov 20, 2008 #2

    Dick

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    Z5? The integers mod 5? Then X and Y can be ANYTHING as long as you pick Z=X+Y-1, can't they? How many solutions is that?
     
  4. Nov 20, 2008 #3
    z5 is mod 5

    i need to find the global solution for that equation?
     
  5. Nov 20, 2008 #4

    Dick

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    There are LOTS of solutions. 1+0-0=1, 1+3-3=1, 4+3-1=1, etc etc. Read my message again.
     
  6. Nov 20, 2008 #5
    how to find a general solution?
     
  7. Nov 20, 2008 #6

    Dick

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    Read my message #2 again. I told you.
     
  8. Nov 20, 2008 #7
    so its (1-y+z,y,z)
    i know that there is endless solutions
    but doesnt mod 5 cuts them
    into 5 solutions?
     
    Last edited: Nov 20, 2008
  9. Nov 20, 2008 #8

    Dick

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    I would say you have 5 different values for Y and five different values for Z, then X is determined. How many possible (Y,Z) pairs?
     
  10. Nov 20, 2008 #9
    25? possibilities
     
  11. Nov 20, 2008 #10

    Dick

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    That would be my answer.
     
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