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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.

June 7th, 2014, 01:55 PM  #3 
Member Joined: Apr 2013 Posts: 52 Thanks: 0  

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apply, division, euclidean 
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