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

Home > Just Math
Constant from Four Solutions (Posted on 2016-04-24) Difficulty: 3 of 5
Determine the minimum value of a positive integer constant K such that the equation:
X*Y2 - Y2 + 2*X + Y = K has precisely four solutions in positive integers.

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Posible solution (2) Comment 2 of 2 |
In my precedent post I've found five solutions for K=60. When I posted I didn't notice that there is always a trivial solution for x=1 as then y+2=K and there is always a pair of integers (x,y) = (1, k-2) for each possible value of K. So I find yself with five solutions instead of four.

But as the problem ask for precisely four solutions I've been trying to find another more fitting answer. The process is quite time consuming (to do it properly) with the way I followed, so I have to give up without been sure about the result.

The lowest set of four solutions I have found are: 

K=258; (x,y) = (86,1) (24,3) (15,4) (1,256) 
(the last is the "trivial solution")

As you can see, K here is higher than K=60 (which has five solutions)

  Posted by armando on 2016-04-27 06:00:14
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 (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2019 by Animus Pactum Consulting. All rights reserved. Privacy Information