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?
$$u_n=\ {a \in\mathbb z_n \mid \gcd (a,n)=1 \}$$ i searched the internet but did.
Aubin, un théorème de compacité, c.r. 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. 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.
