Euler 9 in Go

For fun I picked one of the Euler algorithms I had played with before and rewrote it in Go. Instead of carrying over the nested-loop search, this version first eliminates c using the fixed sum and solves the Pythagorean equation for b. Only a remains to search.

package main

import (
	"fmt"
	"os"
)

func main() {
	const sum = 1000

	for a := 1; a < sum/3; a++ {
		numerator := sum * (sum - 2*a)
		denominator := 2 * (sum - a)

		if numerator%denominator != 0 {
			continue
		}

		b := numerator / denominator
		c := sum - a - b
		if a < b && b < c {
			fmt.Println(a * b * c)
			return
		}
	}

	fmt.Fprintln(os.Stderr, "no solution")
	os.Exit(1)
}

The divisibility check rejects values of a that would produce a fractional b. The program uses constant space, examines fewer than sum / 3 candidates, and prints 31875000.