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The distant graph $G = G(\mathbb{P}(Z),\triangle)$ of the projective lineover the ring of integers is considered. The shortest path problem in thisgraph is solved by use of Klein's geometric interpretation of Euclideancontinued fractions. In case the minimal path is non-unique, all the possiblesplitting are described which allows us to give necessary and sufficientconditions for existence of a unique shortest path.

The Shortest Path Problem for the Distant Graph of the Projective Line Over the Ring of Integers