import scala.math._

def isRightTriangle(longestSide: Int, sideA: Int, sideB: Int): Boolean =
  pow(longestSide, 2).toInt == (pow(sideA, 2) + pow(sideB, 2)).toInt

def countRightTriangles(girth: Int): Int = {
  ((girth / 3).toInt to (girth / 2).toInt).map { l =>
    1 to (girth - l) / 2 count(s => isRightTriangle(l, s, girth - l - s))
  }.sum
}

println(3 to 1000 maxBy(countRightTriangles))
// => 840