Erdős Problem 70: Let $\mathfrak{c}$ be the cardinality of the continuum, let $\beta$ be a countable ordinal, and let $2 \le n < \omega$. Is it true that $\mathfrak{c} \to (\beta, n)^3_2$?

Erdős–Rado partial result: $\mathfrak{c} \to (\omega + n, 4)^3_2$ for any $2 \le n < \omega$. Positive partial answer to Problem 70 with $\beta = \omega + n$ and the blue side fixed at $4$.