OME 1991 Problem 2

Given two distinct elements $a,b \in \{-1,0,1\}$ , consider the matrix $A$ . Find a subset $S$ of the set of the rows of $A$ , of minimum size, such that every other row of $A$ is a linear combination of the rows in $S$ with integer coefficients.

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Dataset text AI-MO AoPS. Quoted with source.

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