Problem 9 of Project Euler

A Pythagorean triplet is a set of three natural numbers, a b c, for which,

a^2 + b^2 = c^2
For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.

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

The Answer

31875000 (a = 200, b = 375, c = 425)

Execution Time

224.3431ms

Source Code

  1. <?php
  2. $k = 1000;
  3. $product = 0;
  4. for($i = 1; $i <= $k; $i++)
  5. {
  6.     for($j = $i + 1; $j <= $k; $j++)
  7.     {
  8.         if( $i*$i + $j*$j == ($k - $i - $j) * ($k - $i - $j) )
  9.         {
  10.             $product = $i * $j * ($k - $i - $j);
  11.             $answer = sprintf("%d (a = %d, b = %d, c = %d)", $product, $i, $j, $k - $i - $j);
  12.             break;
  13.         }
  14.     }
  15. }
  16. echo $answer;
  17. ?>
<?php
$k = 1000;
$product = 0;
for($i = 1; $i <= $k; $i++)
{
	for($j = $i + 1; $j <= $k; $j++)
	{
		if( $i*$i + $j*$j == ($k - $i - $j) * ($k - $i - $j) )
		{
			$product = $i * $j * ($k - $i - $j);
			$answer = sprintf("%d (a = %d, b = %d, c = %d)", $product, $i, $j, $k - $i - $j);
			break;
		}
	}
}
echo $answer;
?>

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