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joaopa
joaopa
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One of my students asked me the following question. It seemed easy to answer but in fact, I am stucK.

The question: does there exist an infinite subset $S$ of $\mathbb N$ such there exists a positive integer $n_0$ such for all prime $p\ge n_0$ one has $$\mathrm{Card}(E \pmod p)<p$$$$\mathrm{Card}(S \pmod p)<p$$ where $E\pmod p$$S\pmod p$ is the subset of classes of $\mathbb Z/p\mathbb Z$ having a representative in $E$$S$.

Thanks in advance (for me and my student :D )

One of my students asked me the following question. It seemed easy to answer but in fact, I am stucK.

The question: does there exist an infinite subset $S$ of $\mathbb N$ such there exists a positive integer $n_0$ such for all prime $p\ge n_0$ one has $$\mathrm{Card}(E \pmod p)<p$$ where $E\pmod p$ is the subset of classes of $\mathbb Z/p\mathbb Z$ having a representative in $E$.

Thanks in advance (for me and my student :D )

One of my students asked me the following question. It seemed easy to answer but in fact, I am stucK.

The question: does there exist an infinite subset $S$ of $\mathbb N$ such there exists a positive integer $n_0$ such for all prime $p\ge n_0$ one has $$\mathrm{Card}(S \pmod p)<p$$ where $S\pmod p$ is the subset of classes of $\mathbb Z/p\mathbb Z$ having a representative in $S$.

Thanks in advance (for me and my student :D )

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joaopa
joaopa
  • 4k
  • 1
  • 16
  • 21

Subset of $\mathbb N$ missing at least a class modulo each prime

One of my students asked me the following question. It seemed easy to answer but in fact, I am stucK.

The question: does there exist an infinite subset $S$ of $\mathbb N$ such there exists a positive integer $n_0$ such for all prime $p\ge n_0$ one has $$\mathrm{Card}(E \pmod p)<p$$ where $E\pmod p$ is the subset of classes of $\mathbb Z/p\mathbb Z$ having a representative in $E$.

Thanks in advance (for me and my student :D )