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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
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