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X=y%z How to solve for y?

  1. Jul 26, 2015 #1
    Hey all, if x=y%z How do i solve for y?
     
  2. jcsd
  3. Jul 26, 2015 #2

    Mentallic

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    Homework Helper

    Take an example:

    [tex]3=12\%9[/tex]

    So in this case we have that x=3, z=9, and y=12. But also,

    [tex]3=3\%9[/tex]
    [tex]3=21\%9[/tex]
    [tex]3=-6\%9[/tex]
    [tex]3=(100*9+3)\%9[/tex]

    Are you seeing the pattern? Can you develop a simple formula that gives us every possible y value that satisfies this equation?
     
  4. Jul 26, 2015 #3
    y=z*i+x, i is int > 0
     
  5. Jul 27, 2015 #4

    HallsofIvy

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    Science Advisor

    Why greater than 0? -6= 3%9 because -6= 3+ (-1)9.

    (I would say "-6= 3 (mod 9). "%" is computer code.)
     
  6. Jul 27, 2015 #5
    Yes, ## y = nz+x## ##∀x,y,z,n ∈ ℤ ## is more inclusive.
     
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