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 June 7th, 2014, 09:17 AM #1 Member   Joined: Apr 2013 Posts: 52 Thanks: 0 Apply the Euclidean division Hey!!!! I am looking at the following exercise: In $\mathbb{Z}_7$ apply the Euclidean division, dividing $2x^5+x^4+3x^3+2x^2+x+1$ by $3x^3+x^2+4x+2$. I made $3x^3+x^2+4x+2$ monic and I got : $x^3+5x^2+6x+3$.  At the first step,I found that: $$2x^5+x^4+3x^3+2x^2+x+1=(x^3+5x^2+6x+3) \cdot (2x^2+5x+1)+(3x^2+x+5)$$ But...according to my note,it is like that: $$2x^5+x^4+3x^3+2x^2+x+1=(x^3+5x^2+6x+3)+(3x^2+6x+ 4)$$ Could you tell me which of them is right?
 June 7th, 2014, 10:49 AM #2 Senior Member   Joined: Mar 2012 Posts: 294 Thanks: 88 The first one. Thanks from evinda
June 7th, 2014, 01:55 PM   #3
Member

Joined: Apr 2013

Posts: 52
Thanks: 0

Quote:
 Originally Posted by Deveno The first one.
Nice!!!Thank you very much!!!

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