Problem 9 - Special Pythagorean triplet

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.

$a=200   $a2=40,000
$b=375   $b2=140,625
$c=425   $c2=180,625
abc = 31,875,000