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I am trying to solve the following diophantine equation

x*a + y*b == c

where a,b,c are integers and the absolute value of their sums is, for instance, 4. Then I like to plot the results in the x,y plane.

Is it possible with FindInstance or Reduce ? Thanks.

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    $\begingroup$ Reduce[{x*a + y*b == c, Abs[a + b + c] == 4}, {x, y}, Integers] returns a result, albeit somewhat complex. Perhaps you could start from there. $\endgroup$
    – MarcoB
    May 29 '16 at 3:40
  • $\begingroup$ What do you mean by "plot the results in the x,y plane"? What kind of plot do you envision? What will be the independent and dependent variable? What parameters? $\endgroup$
    – m_goldberg
    Jun 30 '16 at 0:34