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I have a simple contour plot and wanted to find solutions only when both x and y are integers. The following code doesn't seem to work.

ContourPlot[{4 x == 3 y, {x, y} \[Element] Integers}, {x, 0, 20}, {y, 0, 20}]

For the above code I was expecting the plot to have a few dots that satisfy the equations, instead the code just gives a continuous line.

How would I do it?

thanks,

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    $\begingroup$ ListPlot[{x, y} /. Solve[{4 x == 3 y, 0 <= x <= 20, 0 <= y <= 20}, {x, y}, Integers]]? $\endgroup$
    – kglr
    Commented May 26, 2016 at 3:35

1 Answer 1

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ContourPlot[{4 x == 3 y, {x, y} ∈ Integers},
 {x, 0, 20}, {y, 0, 20},
 ContourStyle -> Thin, Epilog -> {Red, AbsolutePointSize[6],
   Tooltip[Point[#], #] & /@
    ({x, y} /. 
      Solve[{4 x == 3 y, 0 <= x <= 20, 0 <= y <= 20},
       {x, y}, Integers])}]

enter image description here

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