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Problem #253: Let $a_1

Let $a_1

Problem Statement

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 $a_i$.
Categories: Number Theory

Progress

This was disproved by Cassels [Ca60].

Source: erdosproblems.com/253 | Last verified: January 14, 2026

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