# How to do this Sagemath task about Rings and Polynomials?

1) compute 17^100 + 21^30 · 55 in Z/35Z. Hint: you can use the parent “Intergers(35)”.

2) Let p = x^3 −14x^2 +59x−70. Factorize p.

3) Turn p into a polynomial over Z and save it as q. So “q.parent()” should be “Univariate Polynomial Ring in x over Integer Ring.”

4) Use a different method to turn p into a polynomial over F7 and save it as r.

5) compute the roots of p, q and r separately.