Erdős Problem 1198 #7406

What is the Erdős problem?

https://www.erdosproblems.com/1198

If $\mathbb{N}$ is $2$-coloured then must there exist an infinite set $A={a_1<a_2<\cdots}$ such that all expressions of the shape $\sum_{j=1}^{k}\prod_{i\in S_j}a_i$, where $S_1,\ldots,S_k$ are pairwise disjoint sets of indices (excluding the trivial expressions $a_i$), are the same colour?

Status: solved

AMS categories

• ams-5
• ams-11

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