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Decide a positive integer $N \in\mathbb Z$. Generate a uniformly distributed random positive integer sequence: $$v_1, v_2, \ldots,v_n\in\mathbb Z_N$$ My question is, what does $\mathbb Z_N$ really mean here? Does it mean something like the set of integers up to $N$?

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  • $\begingroup$ It totally depends upon context, but often $\mathbb Z_n$ refers to the integers modulo n. $\endgroup$ – Fredrik Meyer May 5 '13 at 17:59
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    $\begingroup$ Is it $\mathbb Z_N$? Then it should better be written $\mathbb Z/N\mathbb Z$ to avoid confusion with certain other notations and refers to integers modulo $N$, which can be represented by the integers $0, 1, \ldots, N-1$. $\endgroup$ – Hagen von Eitzen May 5 '13 at 18:05
  • $\begingroup$ okay!yes thank you so much.Got it, it is indeed integers modulo N,which would me the same set as integers less than N $\endgroup$ – user1736473 May 5 '13 at 18:09
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Most often, one sees $\mathbb Z_n$ used to denote the integers modulo $n$, represented by $\mathbb Z_n = \{0, 1, 2, \cdots, n-1\}$: the non-negative integers less than $n$. So this correlates with the set you discuss, in that we have a set of $n$ elements, but here, we start at $n = 0$ and increment until we reach $n - 1$, where we stop, (since $n \equiv 0\pmod n$).

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