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

Home > Just Math
Expression Quotient Puzzle (Posted on 2015-06-16) Difficulty: 3 of 5
Find all pairs (x,y) of positive integers x and y such that:
x + y + 1 divides 2xy and:
x + y − 1 divides x2 + y2 − 1

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Some, maybe all | Comment 1 of 3
By symmetry if (x,y) works then (y,x) works.

If y=x+1 then
x+(x+1)+1 = 2(x+1) divides 2x(x+1) and
x+(x+1)-1 = 2x divides x2 + (x+1)2 − 1 = 2x(x+1)

so all of (x,x+1) and (x,x-1) works.

There appear to be other sporadic cases to each of the two divisions, but I haven't found any in common yet.

  Posted by Jer on 2015-06-16 09:30:04
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 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information