I'm having enormous trouble with this. Any help appreciated.

GCD of:

(x^4)+x+1 and (x^2)+x+1 in Z2(x).

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- Oct 22nd 2006, 12:19 PMJaysFan31Greatest Common Divisor of polynomial
I'm having enormous trouble with this. Any help appreciated.

GCD of:

(x^4)+x+1 and (x^2)+x+1 in Z2(x). - Oct 22nd 2006, 02:40 PMtopsquark
It looks fairly simple to me. Using the Euclidean Algorithm I get that

$\displaystyle x^4+x+1 = (x^2 - x)(x^2 + x + 1) + 1$

So r1 = 1.

Then

$\displaystyle x^2+x+1 = (x^2+x+1)(1) + 0$

So r2 = 0.

This means that the GCD is r1 = 1. (ie. They are relatively prime.)

-Dan - Oct 22nd 2006, 03:05 PMtopsquark