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.)
solution | Comment 2 of 3 |
quick search of all combinations of remainders for x,y mod 17 gives that only when (x,y) mod 17 is (0,0), (3,2), or (5,3) is both of the given expressions divisible by 17.

For each of these 3 combinations, xy-12+15y is also divisible by 17.

Thus it is always true.

  Posted by Daniel on 2015-04-27 11:23:51
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 (10)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information