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

Home > Numbers
Discriminants (Posted on 2005-05-24) Difficulty: 2 of 5
Consider a quadratic equation with integer coefficients.
Is every integer a possible discriminant?

Prove it.

  Submitted by Jer    
Rating: 3.5000 (4 votes)
Solution: (Hide)
Only integers congruent to 0 or 1(mod 4) are possible.

If b is even b^2 is a multiple of 4 so b^2-4ac is a multiple of 4
If b is odd, then b=2k+1 so b^2 is 4k^2 + 4k + 1 which is congruent to 1(mod4) and so b^2-4ac is too.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionPuzzle SolutionK Sengupta2009-01-22 13:58:12
A further noteJer2005-06-08 16:56:26
Some Thoughtsre(2): FourBractals2005-05-27 05:02:39
re: FourRichard2005-05-25 09:10:41
SolutionFourBractals2005-05-25 05:24:26
re: Solution (no explanation given)Richard2005-05-24 22:47:51
SolutionSolution (no explanation given)Old Original Oskar!2005-05-24 14:11:21
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