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Let $ \{x_{n}\}$ be a sequence in $ \mathbb{N}$ with $ x_{1}=1$ such that for any prime $ p$ , the set $ $ A=\{x_{1},x_{2},\ldots,x_{p}\}$ $ forms a complete residue system $ \pmod{p}$ . Now is it true that $ \lim\limits_{n\to\infty}\frac{x_{n}}{n}$ exists for any natural number $ n$ ? If yes what is it’s value?Read more