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edited tags, clarified notation, wrote more precise title
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YCor
YCor
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Want an Large arithmetic progression under a setmodulo $p$

Let $B$ be a subset of $Z_p$$Z_p(=\mathbb{Z}/p\mathbb{Z})$ of lengthcardinal $Cp^{\frac{1}{3}}$, for some constant $C$. How to construct an arithmetic progression of length $C_1p^{\frac{2}{3}}$ where $C_1$ is some constant, inside $B+\alpha B$ for any $\alpha \in Z_p$ ?

Want an arithmetic progression under a set

Let $B$ be a subset of $Z_p$ of length $Cp^{\frac{1}{3}}$, for some constant $C$. How to construct an arithmetic progression of length $C_1p^{\frac{2}{3}}$ where $C_1$ is some constant, inside $B+\alpha B$ for any $\alpha \in Z_p$ ?

Large arithmetic progression modulo $p$

Let $B$ be a subset of $Z_p(=\mathbb{Z}/p\mathbb{Z})$ of cardinal $Cp^{\frac{1}{3}}$, for some constant $C$. How to construct an arithmetic progression of length $C_1p^{\frac{2}{3}}$ where $C_1$ is some constant, inside $B+\alpha B$ for any $\alpha \in Z_p$ ?

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Eshita Mazumdar
Eshita Mazumdar
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Want an arithmetic progression under a set

Let $B$ be a subset of $Z_p$ of length $Cp^{\frac{1}{3}}$, for some constant $C$. How to construct an arithmetic progression of length $C_1p^{\frac{2}{3}}$ where $C_1$ is some constant, inside $B+\alpha B$ for any $\alpha \in Z_p$ ?