Find Two Numbers that Equal the Sum of the Rest in JavaScript

Suppose following is the problem:

We have a sequence of numbers starting from 1 and upto any arbitrary number, let's call it num. We have to pick two such numbers from the sequence (let's call them m and n), such that:

sum(1 to num) - (m + n) = m * n

And finally, we should return an array of groups of all such numbers.

For example −

If the input is −

const num = 10;

Then the output should be −

const output = [
   [7, 6]
];

because sum(1 to 10) = 55

and,

55 - (6 + 7) = 6 * 7 = 42

Example

The code for this will be −

 Live Demo

const num = 10;
const pickNumbers = num => {
   const sum = (num) * (num + 1) * (.5);
   const results = [];
   for (let n = 1; n <= num; n++) {
      let first = sum - n;
      let second = n + 1;
      if (first % second === 0) {
         let m = first / second;
         if (m < num && m !== n && results.every(group => group[0] + group[1]
         !== m + n)){
            results.push([m, n]);
         }
      }
   }
   return results;
}
console.log(pickNumbers(10));

Output

And the output in the console will be −

[
   [7, 6]
]