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

Home > Just Math
Seventeen divides expression? (Posted on 2015-04-26) Difficulty: 3 of 5
x, y are integers, and 17 divides both the expressions x2-2xy+y2-5x+7y and x2-3xy+2y2+x-y.

Does 17 always divide xy-12x+15y, for every choice of x and y?

If not, give an example.
If so, prove it.

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Hints/Tips A solution | Comment 1 of 3

Answer: Yes, xy-12x+15y is always divisible by 17 under the given conditions; for example, x=3080, y=1719 is just one possible solution.

The proof is straightforward and is left to the reader.

  Posted by broll on 2015-04-26 12:39:00
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 (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

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