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arXiv · 1611.06414

An upper bound for weak $B_k$-sets

Tomasz Schoen·Ilya D. Shkredov
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Abstract

We prove that if $A\subseteq \{ 1,2,\dots, N \}$ does not contain any solution to the equation $x_1+\dots+x_k=y_1+\dots+y_k$ with distinct $x_1,\dots,x_k,y_1,\dots,y_k\in A$, then $|A|\ll {k^{3/2}}N^{1/k}.$

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Tomasz Schoen, Ilya D. Shkredov. 2016-11-19. An upper bound for weak $B_k$-sets. https://arxiv.org/abs/1611.06414

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