Each of the three positive integers (81+K), (162+K) and (337+K) is a perfect square such that their positive square-roots are in

**harmonic sequence**.

Determine the value of K, and prove that no other value for K is possible.

(In reply to

re: Solution by Math Man)

If n=0, then K=-81, so K+81=0 is a square

0 is not a ** ****positive integer.**