Erdős Problem #829

Let $A\subset\mathbb{N}$ be the set of cubes. Is it true that\[1_A\ast 1_A(n) \ll (\log n)^{O(1)}?\]

number theory

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Mordell proved that\[\limsup_{n\to \infty} 1_A\ast 1_A(n)=\infty\]and Mahler [Ma35b] proved\[1_A\ast 1_A(n) \gg (\log n)^{1/4}\]for infinitely many $n$. Stewart [St08] improved this to\[1_A\ast 1_A(n) \gg (\log n)^{11/13}.\]

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This page was last edited 14 October 2025.

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Additional thanks to: msellke

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