Thread: My guess ... easy proof ?

This is my guess , i hope that's true .

Let's say a triangle is a Heron triangle if the lengths of its three sides as well as its area
are integers.

I guess : If are primes such that , then all the non-isosceles Heron triangles with as the length of one of the sides are right-angled . Therefore , we can only find out one or two possible Heron triangle(s) for it .

For example , let we have

Then the only Heron triangles are ?

How about or ?

EDIT (Oops!):

and is not prime.
and [LaTeX ERROR: Convert failed] is not prime.

Oh , i missed a thing so what i guessed is not necessarily correct !

For example , but is not right-angled .

Had it been true, it would have been a curiously nice result; and we would have called it Simplependulum's
postulate (because it oddly reminded me of Bertrand's postulate). Keep guessing, my friend; keep guessing!