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Non-rational Quadratic (Posted on 2010-08-22) Difficulty: 2 of 5
Prove that the quadratic equation ax2 + bx + c = 0
does not have a rational root if a, b, and c are odd integers.

See The Solution Submitted by Bractals    
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re: Mod 4 | Comment 4 of 5 |
(In reply to Mod 4 by Ady TZIDON)

Ady:


I'd be interested in your Mod 4 proof, since I couldn't make that work, and I have doubts that it does work. 

 b^2-4*a*c = 1 (mod 4), so it looks like it could conceivably be a square.

Plus, 4ac = 0 (mod 4), even if a or c are even, which is another reason I doubt it will work.

But I'd like to be proved wrong,

Steve

  Posted by Steve Herman on 2010-08-23 13:32:10
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