Posted on Tue, 20/12/2011 - 15:17
Question
A Pythagorean triplet is a set of three natural numbers, a 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
$product = 0;
for ($i = 2;; $i++) {
for ($j = 1; $j < $i; $j++) {
$a = ($i * $i) - ($j * $j);
$b = 2 * $i * $j;
$c = ($i * $i) + ($j * $j);
if ($a + $b + $c == 1000) {
$product = $a * $b * $c;
break 2;
}
}
}
echo $product;Time taken to execute: 0.0003 second.
Answer
31875000
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