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Answer by Elaqqad for Covering $\mathbb{N}$ with disjoint arithmetic sequences
The equality $2$ can be determined using the observation that the sum of all elements belonging to each set $S_i$ is the sum of all residues so:$$...
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Suppose that we have a collection $S_1 = \{a_1 + kr_1\}_{k=0}^{\infty}$, $\cdots$, $S_n = \{a_n + kr_n\}_{k=0}^{\infty}$ of disjoint arithmetic sequences where $a_i$, $r_i$ are nonnegative integers for...
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