Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.

Updated Oct 7

Problem 11

Statement. Is every large odd integer $n$ the sum of a squarefree number and a power of 2?

Status. Open.

Source. erdosproblems.com/11, accessed 2026-09-04. Cite as: T. F. Bloom, Erdős Problem #11, https://www.erdosproblems.com/11.

References.

[GrSo98] Granville, A. and Soundararajan, K., [[../library/additive_bases/granville_1998_binary_additive_problem_erdos_order_2_mod_p_2/_index|A Binary Additive Problem of Erdős and the Order of $2$ mod $p^2$ ]]. The Ramanujan Journal (1998), 283-298.
[Gu04] Guy, Richard K., Unsolved problems in number theory. Third edition, Problem Books in Mathematics, Springer, New York (2004), xviii+437 pp.; section A19 "Values of $n$ making $n-2^k$ prime. Odd numbers not of the form $\pm p^a\pm2^b$ .", printed p. 67: the question whether some odd integer is not of the form $2^k+s$ with $s$ squarefree, with no example found below $1.4\cdot10^9$ . Library home: guy_2004_unsolved_problems_number_theory.
[He24b] C. Hercher, On the Sum of Squarefree Integers and a Power of Two. arXiv:2411.01964 (2024).

Formalization. Statement in formal-conjectures.

Progress

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These entries are derived from explicit links on library pages. They are navigation only and do not by themselves record mathematical progress.

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