Erdős Problem #532

If $\mathbb{N}$ is 2-coloured then is there some infinite set $A\subseteq \mathbb{N}$ such that all finite subset sums\[ \sum_{n\in S}n\](as $S$ ranges over all non-empty finite subsets of $A$) are monochromatic?

#532: [Er73][Er75b][Er77c]

number theory | ramsey theory

In other words, must some colour class be an IP set. Asked by Graham and Rothschild. See also [531].

Proved by Hindman [Hi74] (for any number of colours).

See also [948].

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