Thread: Greatest 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).

Originally Posted by JaysFan31

I'm having enormous trouble with this. Any help appreciated.
GCD of:
(x^4)+x+1 and (x^2)+x+1 in Z2(x).

It looks fairly simple to me. Using the Euclidean Algorithm I get that

So r1 = 1.

Then

So r2 = 0.

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

-Dan

Originally Posted by topsquark

It looks fairly simple to me. Using the Euclidean Algorithm I get that

So r1 = 1.

Then

So r2 = 0.

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

-Dan

Another way to check this is to note that is irreducible in Z2[x].

-Dan