Homework 18

Read: Finish Section 4.1, read Section 4.2, and start Section 4.3.

Turn in: 4.46, 4.47, 4.49, 4.51, 4.58, 4.71, 4.75

• For 4.49, 4.58, you may want to use 4.47, but to do that, you need to select a generator $g$ for $\mathbb{Z}_m$ and translate the notation $g^k$ to additive notation. Note that $1$ is always a generator for $\mathbb{Z}_m$, and additively, $1^k$ should be written $k\cdot 1 = k$. Also, if you want another reference for modular arithmetic, you could see if my Math 102 notes about congruences help at all.

Extra practice: Problems/Theorems we skipped in Sections 4.1 and 4.2