Erdős Problems

Browse all problems

↑ ↓ to move↵ to openesc to close

Loading problem…

Status

On this page

Status

Topics

Terms Privacy info@plasma.ai

Problem 845 — Erdős Problems

Problem 845

Let $C>0$ . Is it true that the set of integers of the form

n=b_1+\cdots+b_t\textrm{ with }b_1<\cdots<b_t

where $b_i=2^{k_i}3^{l_i}$ for $1\leq i\leq t$ and $b_t\leq Cb_1$ has density $0$ ?

Source: erdosproblems.com/845

Number theory

Wiki page

Status

Solved·, Disproved

An accepted solution exists. The statement is false.

DISPROVED (LEAN).

Er92b: Erdős, Paul, Some of my favourite problems in various branches of combinatorics. Matematiche (Catania) (1992), 231-240.
ErLe96: Erdős, P. and Lewin, Mordechai, $d$ -complete sequences of integers. Math. Comp. (1996), 837-840.
vDEv25: W. van Doorn and A. Everts, Smooth sums with small spacings. arXiv:2511.04585 (2025).

Proof claims

Loading proof claims…

Discussion

Loading discussion…

PreviousProblem 844 NextProblem 846

On this page

Statement
Status
References
Proof claims
Discussion

Status: Solved, Disproved
Topics: Number theory
In the wiki: Wiki page