Abstract
To end our story about Markov numbers, we turn to the second theme, the uniqueness conjecture. We have seen several different versions ranging from numbers and matrices to hyperbolic geometry and matchings of graphs. The uniqueness results in Chapters 3 and 4 were based directly on the Markov equation and some simple congruences derived from it. Now we want to take a closer look at some of the systematic approaches attempted so far. They are arranged in three groups of increasing complexity:
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