Exercise 2.3.4 ( Generators of $\mathbb{Z}/202\, \mathbb{Z}$)

Proof. The generators of $\mathbb{Z}∕202\mathbb{Z}$ are the elements $\bar{d}\in \mathbb{Z}∕202\mathbb{Z}(0\le d<202)$ such that $d\wedge 202=1$ (i.e, since $101$ is a prime number, such that $2\nmid d,101\nmid d$). This gives all the odd integers of $[[1,201]]$, except $101$, so there are $100$ such numbers.

(As a verification $\phi (202)=\phi (101)\phi (2)=(101-1)(2^1-1)=100$, so there are $100$ generators of $\mathbb{Z}∕202\mathbb{Z}$.) □