What Generates the Ideal in Q[X] with Polynomials x^2+1 and x^6+x^3+x+1?

[iNCREDiBLE]

Consider the ideal I of Q[x] generated by the two polynomials f = x^2+1 and g=x^6+x^3+x+1

a) find h in Q[x] such that I=<h>
b) find two polynomials s, t in Q[x] such that h=sf+tg

 

[Euclid]

Have you even given this problem a shot? It's fairly easy.
Consider the ideal I of Z generated by 12 and 20. Do you know how to find a single number x that generates I? If you can't do this, you won't be able to do this problem either.