## Compute large powers modulo n

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.2 Exercise 3.2.23 Determine the last two digits of $3^{3^{100}}$. (Find $3^{100} \mod {\varphi(100)}$ and use Exercise 3.2.22.) Solution:…

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.3 Exercise 3.3.6 Let $M = \langle u,v \rangle$ be the modular group of order 16 described in Exercise…