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June 7th, 2014, 09:17 AM   #1
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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?
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June 7th, 2014, 10:49 AM   #2
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The first one.
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June 7th, 2014, 01:55 PM   #3
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Originally Posted by Deveno View Post
The first one.
Nice!!!Thank you very much!!!
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