Problem

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.

Solution

for ($a = 1; $a < 500; $a++) {
for ($b = $a + 1; $b < 500; $b++) {
$c = 1000 - $a - $b;
if ($c > $b && $b > $a && $a * $a + $b * $b == $c * $c) {
break 2;
}
}
}

echo $a * $b * $c;