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.
(In reply to
A start? by DJ)
The equation that you have got, that is, c=aČ/x + a, gives you a third degree equation in a and may be using Cardan's method might help or may be using that makes it more complicated ? I haven't tried that yet, because I am thinking of some different method to solve this problem. It was just a suggestion. if anyone knows that method, he/she can give it a try.
re: A start?
