/**
 * 
 * Ashish Patel
 * e: ashishsushilPatel@gmail.com
 * w: https://ashish.me
 *
 */

/* 
Fermat's factorization method is: If a · b = n (where a ≤ b), then there exist some c and d such that n = c^2 - d^2. 
Your goal is to return for given n such c and d as an array. Since we want c and d to be uniquely determined, in all test cases n is a semiprime number.

Example

For n = 15, the output should be fermactor(n) = [4, 1]. 15 = 4^2 - 1^2.
*/

function fermafactor(n) {
  for (let i = 1; i < n; i++) {
    for (let j = 1; j < n; j++) {
      const sum = Math.pow(i,2) - Math.pow(j,2)
      if(n === sum){
        return [i,j]
      }
    }
  }
}

test('fermafactor', () => {
  expect(fermafactor(15)).toEqual([4,1])
});