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.

Start with ((2M – N)/(2M + N)), ignoring everything else.

Let n = ((2M – N)/(2M + N)), requiring n to be positive, since it is a square root leading to a prime solution. M and N are required to be positive anyway.

But if so, then N = -(2M(n-1)))/(n+1), which cannot be positive. So it looks as though the problem falls at that hurdle.

I'm not seeing how to get past this to the rest of the problem.

Posted by broll on 2016-01-14 23:09:18