Erdős Problem #941

Are all large integers the sum of at most three powerful numbers (i.e. if $p\mid n$ then $p^2\mid n$)?

number theory | powerful

This was given in 1986 in the Oberwolfach problem book as a problem of Erdős and Ivić. It was proved by Heath-Brown [He88].

See [1107] for the generalisation to $r$-powerful numbers with $r\geq 3$, and also [940].

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This page was last edited 03 November 2025.

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T. F. Bloom, Erdős Problem #941, https://www.erdosproblems.com/941, accessed 2025-12-07