There seems to be an error in the following calculation, I'm not quite sure what it is though. Could someone point it out?
Thanks.
Find the GCD of p(x) = 2x^5 + x^3 + 2^x + 1 and q(x) = x^4 + x^3 + x + 1 in z3[x]
Use the Euclidean algorithm:
2x^5 + x^3 + 2x + 1 = (2x + 1)(x^4 + x^3 + x + 1) + x^2 + 2x
x^4 + x^3 + x + 1 = (x^2 + 2x + 2)(x^2 + 2x) + 1
x^2 + 2x = (1)(x^2 + 2x) + 0
So the answer is 1
I was told there was something wrong with the calculation, but didn't really get a proper explanation of why. I'm quite sure that the first two lines are right, and the answer should be too. So that really only leaves the third row
x^2 + 2x = (1)(x^2 + 2x) + 0
But it's really simple, so how could it be wrong.. It drives me mad
Oh, and I noticed I wrote 2^x instead of 2x in the initial description, it should be 2x as in the calculation. Sorry about that.