Erdős Problem #253

Let $a_1<a_2<\cdots $ be an infinite sequence of integers such that $a_{i+1}/a_i\to 1$. If every arithmetic progression contains infinitely many integers which are the sum of distinct $a_i$ then every sufficiently large integer is the sum of distinct $a_i$.

#253: [Er61]

number theory

This was disproved by Cassels [Ca60].

View the LaTeX source

External data from the database - you can help update this
Formalised statement? Yes

0 comments on this problem

Likes this problem	None
Interested in collaborating	None
Currently working on this problem	None
This problem looks difficult	None
This problem looks tractable	None

When referring to this problem, please use the original sources of Erdős. If you wish to acknowledge this website, the recommended citation format is:

T. F. Bloom, Erdős Problem #253, https://www.erdosproblems.com/253, accessed 2026-01-16