Special Pythagorean triplet
Problem 9Published on Friday, 25th January 2002, 06:00 pm; Solved by 200409; Difficulty rating: 5%
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.