// multi-utility computation suite · offline · instant · precise
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math.linear-diophantine Calculator
Solves linear Diophantine equations (ax + by = c) for integer solutions, determining whether solutions exist and finding the general solution via extended Euclidean algorithm. Solutions exist if and only if gcd(a,b) divides c — if they exist, there are infinitely many.
Inputs
A
Reference formula or conversion factor shown for context.
B
Reference formula or conversion factor shown for context.
C
Reference formula or conversion factor shown for context.
X0
Reference formula or conversion factor shown for context.
Results
solutions exist?
Sample size or count used in the calculation.
GCD(a,b)
GCD (greatest common divisor) -- the largest integer that divides both numbers with no remainder. Used in fraction simplification and modular arithmetic.
reduced:
Reference formula or conversion factor shown for context.