Erdős · problems
OEIS index →← the campaignThe Erdős problems.
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#949Let $S\subset \mathbb{R}$ be a set containing no solutions to $a+b=c$. Must there be a set $A\subseteq \mathbb{R}\backslash S$ of cardinality continuum such that $A+A\subseteq \mathbb{R}\backslash S$?ramsey theory · 1 Vela attempt (partial proof) · AI tried (unverified) · N/A#965Is it true that, for any $2$-colouring of $\mathbb{R}$, there is a set $A\subseteq \mathbb{R}$ of cardinality $\aleph_1$ such that all sums $a+b$ with $a\neq b$ and $a,b\in A$ are the same colour?ramsey theory · solved · N/A