Special Pythagorean Triplet

Project Euler Problem 9

A Pythagorean triplet is a set of three natural numbers, a < b < c, for which, a2 + b2 = c2

For example, 32 + 42 = 9 + 16 = 25 = 52.

There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc such that a + b + c = n.

This was a tough problem that I spent quite a bit of time on. My original solution involved getting the factors for a the number of interest, but it turned out to be the wrong approach.

The right approach is to use some algebra on paper to pull apart the Pythagorean theorem. The link from StackOverflow below has a great explanation of how to do this.

Here’s what the answer is based on, with some modifcations Stack Overflow

function specialPythagoreanTriplet(n) {
   for(let a = 1; a < n/2; a++){
    for(let b = a; b < n; b++){
      let c = Math.sqrt(a * a + b * b);
      if(c > b && Number.isInteger(c) && a + b + c == n){
        return (a * b * c);
      }
    }
  }
}

specialPythagoreanTriplet(24) // 480
specialPythagoreanTriplet(120) // 49920
specialPythagoreanTriplet(1000) // 31875000