# diophantine linear equation with condition on the sum of coefficients [closed]

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.

## closed as off-topic by MarcoB, m_goldberg, user9660, Öskå, JensJul 1 '16 at 4:14

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• "This question cannot be answered without additional information. Questions on problems in code must describe the specific problem and include valid code to reproduce it. Any data used for programming examples should be embedded in the question or code to generate the (fake) data must be included." – m_goldberg, Community, Öskå, Jens
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• 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. – MarcoB May 29 '16 at 3:40
• 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? – m_goldberg Jun 30 '16 at 0:34