Given a right triangle with lengths that are reciprocals of integers, what is the smallest possible sum of these the integers?

In other words, given a right triangle with lengths 1/a, 1/b, and 1/c, where a, b, and c are all integers, what is the lowest value of a+b+c? Also, prove it.

Taken from CAML, which did not ask for a proof.

I tried lots of fancy stuff (like a²/c² - a²/b² = 1) but it didn't seem to help me as much as my simple equation.

You can read the lower posts if you want to learn more :)

Posted by Gamer on 2003-08-06 03:46:24