Origin - http://alpha.math.uga.edu/~pete/4400FULL.pdf - on p120, Theorem 122
Fix a positive integer $N>2$, and let $H$ be a proper subgroup of $U(N)=(Z/NZ)^{\times}$.
There are infinitely many primes $p$ such that $p(mod\ N)\not\in H$.
The proof is left as an exercise. Suggestion: fix $a\in Z^{+},\ 1<a<N$, such that $a (mod\ N)\not\in H$. Take $P_{0}=2N+a$ and for $n\geq 1,\ P_{n}=(2N\displaystyle \prod_{i=1}^{n}p_{i})+a.$
(1) Is there a full proof of this theorem - I want to look at one first to try to edify myself on the origins of $P_{0}=2N+a$ and $P_{n}=(2N\displaystyle \prod_{i=1}^{n}p_{i})+a$. I googled. Is there a name for this?
(2) What does $^{\times}$ mean in $U(N)=(Z/NZ)^{\times}$?
This generalizes https://math.stackexchange.com/a/195420/85100 and Proof - There're infinitely many primes of the form 3k + 2 — origin of $3q_1..q_n + 2$.
