9

Problem

A Pythagorean triplet is a set of three natural numbers, a < b < c, for which, a^2+b^2=c^2.

For example, 32 + 42 = 9 + 16 = 25 = 52.

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

Questions

1. Are there any rules for Pythagorean triples?
   1. Like, is there an efficient way to find them?

Ideas/Constraints

1. A or B or C < 998
   1. if A is > 998, then b or c has to be 0 and that does not work
2. Also if A = n then B + C + n is < 998