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Maximum Value Muse (Posted on 2016-01-14) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts Hmmm. | Comment 1 of 10

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
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