All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
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    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
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

Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2021 by Animus Pactum Consulting. All rights reserved. Privacy Information