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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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surprise Comment 10 of 10 |
The puzzle reserves a tricky final because the formula 

P = (N/4)*√((2M-N)/(2M + N))

involves only 2M and N as variables. It turns out that there is an infinite number of pairs (2M, N) resulting in P prime.

So the formula is satisfied by all the pairs (2M, N) = (5K, 4K) con K=3p e p any prime.

But then 2M is always odd, so that M is not an integer.

And then the only other solution is M=20, N=24, P=3.


Edited on March 3, 2016, 11:40 am
  Posted by armando on 2016-03-03 04:46:03

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