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Finding all solutions of a Diophantine equation using JavaScript
Problem
We are required to write a JavaScript function that takes in a number n. Our function should find all such number x and y such that −
x^2 - 4y^2 = n.
And it should return an array of all such pairs.
Example
Following is the code −
const num = 90005;
const findSolution = (num = 1) => {
const res = [];
let a, b;
for(let a = 1; a <= Math.sqrt(num); a++){
if(Number.isInteger(b = num/a)){
if(Number.isInteger(x = (b+a)/2)){
if(Number.isInteger(y = (b-a)/4)){
res.push([x, y]);
};
};
};
};
return res;
};
console.log(findSolution(num));Output
[ [ 45003, 22501 ], [ 9003, 4499 ], [ 981, 467 ], [ 309, 37 ] ]
Updated on: 19-Apr-2021
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