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.
We all know that the three pythagorean triplets are expressed in the form: n, (n²-1)/2 and (n²+1)/2, where 'n' is a positive odd integer and the number (n²+1)/2 being the greatest, is the hypotenuse.
So the three sides I know can be expressed in the above form when it is given that the three sides are integral but I do not know in which form am I supposed to express the lengths of the sides of a right triangle if they are fractional as in the given problem.
This was just a hint (may be a useless one) but may be someone can get to some result using the fact.
My Idea
