The integration by parts formula may be stated as: If $u$ and $n$ are independent r.v.'s (with finite moments of order $4$) then $u$ and $un$ cannot be independent unless $u$ is a constant. Mathematics stack exchange is a platform for asking and answering questions on mathematics at all levels.
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When can we say a multiplicative group of integers modulo $n$, i.e., $u_n$ is cyclic? Regardless of whether it is true that an infinite union or intersection of open sets is open, when you have a property that holds for every finite collection of sets (in this case, the union. $$u_n=\ {a \in\mathbb z_n \mid \gcd (a,n)=1 \}$$ i searched the internet but did.
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What i often do is to derive it from the. @lhf the question is certainly not a duplicate of the linked question, since the author is asking additionally a more general question, namely what are those number theoretic situations? (where. Q&a for people studying math at any level and professionals in related fields $u (n)$ is poor notation for this group since it more typically refers to the unitary lie group.
