Each of M and N is a positive integer such that:
P = (N/4)*√((2M – N)/(2M + N)) is a prime number.

Determine the maximum possible value of P and prove that no higher value of P is possible.

(In reply to A better try by armando)

In your solution you assert that 2M-N and 2M+N are both squares, namely a^2 and b^2.  How do account for the fact that it is possible for the quotient (2M-N)/(2M+N) to be a rational square but not 2M-N and 2M+N individually?  [For example M=5, N=8 yields (2M-N)/(2M+N) = (10-8)/(10+8) = 2/18 = 1/9 = (1/3)^2].

Posted by Brian Smith on 2016-03-02 00:14:27