Solve linear Diophantine equations
ax + by = c
npm: npm i diophantine
– npmjs.com/diophantine
Documentation: kevduc.github.io/diophantine
GitHub: kevduc/diophantine
Example
example.js
const { dioSolve, SolutionType } = require('diophantine')
const a = 59
const b = -7
const c = 4
console.log(`Solving: ${a}x + ${b}y = ${c}`)
const { solutionType, g, z, m, p } = dioSolve(a, b, c)
switch (solutionType) {
case SolutionType.None: {
console.log(`No solution (gcd = ${g} ∤ c = ${c})`)
break
}
case SolutionType.Unique: {
console.log(`Unique solution: ${z[0] !== null ? `x = ${z[0]}` : `y = ${z[1]}`}`)
break
}
case SolutionType.Linear: {
console.log(` gcd = ${g}`)
console.log(` x0 = ${z[0]}, y0 = ${z[1]}`)
console.log(` ${a} × ${z[0]} + ${b} × ${z[1]} = ${z[0] * a + z[1] * b}`)
console.log(`Solutions: x = ${m[0]}n + ${p[0]}, y = ${m[1]}n + ${p[1]}`)
break
}
default: {
console.log(`Solution: ${solutionType}`)
break
}
}
Console output
Solving: 59x + -7y = 4
gcd = 1
x0 = -8, y0 = -68
59 × -8 + -7 × -68 = 4
Solutions: x = 7n + 6, y = 59n + 50