MathDB

Let

r

be a positive integer. Find the smallest positive integer

m

satisfying the condition: For all sets

A_1, A_2, \dots, A_r

with

A_i \cap A_j = \emptyset

, for all

i \neq j

, and

\bigcup_{k = 1}^{r} A_k = \{ 1, 2, \dots, m \}

, there exists

a, b \in A_k

for some

k

such that

1 \leq \frac{b}{a} \leq 1 + \frac{1}{2022}

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