All about
flooble

fun stuff

Get a free chatterbox

Free JavaScript

Avatars
perplexus
dot
info
Home
>
Just Math
Expression and Perfect Square (
Posted on 20151010
)
Each of X, Y and Z is a nonzero integer such that:
Z = X + Y/X – 1/Y is an integer.
Is Z always a perfect square?
Give reasons for your answer.
No Solution Yet
Submitted by
K Sengupta
No Rating
Comments: (
Back to comment list
 You must be logged in to post comments.
)
Thoughts
 Comment 1 of 2
it's easy enough to show x=z=y^2 is a solution. The trick is to show there are no other solutions.
A possible line of attack is to solve for x. The resulting quadratic's discriminant is a square if z=y^2. But again, how to show that's the only way?
Posted by
Jer
on 20151011 09:43:26
Please log in:
Login:
Password:
Remember me:
Sign up!

Forgot password
Search:
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
Chatterbox:
blackjack
flooble's webmaster puzzle
Copyright © 2002  2018 by
Animus Pactum Consulting
. All rights reserved.
Privacy Information