Nonnegative Integer Equation Calculator
Count and enumerate nonnegative whole solutions of aX+bY=c with an exact extended-Euclidean calculation.
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Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Use BigInt extended Euclid and exact signed floor/ceiling bounds, showing at most the first 100 nonnegative solutions.
g=gcd(a,b); if g divides c, x=x0+k b/g and y=y0−k a/g; bound k by x,y≥0
Worked example
3X+5Y=30 has three nonnegative solutions: (10,0),(5,3),(0,6).
Assumptions and input details
Positive coefficients and nonnegative target only. Zero solutions is a valid result. All input bounds are safe whole numbers; exact solution coordinates are displayed as integer strings. This is a two-variable count, not an arbitrary integer program.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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