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castor
castor
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Consider the equation $x^2+ay^2+bz^2=(1+a+b)xyz.$ If $(1,1,1)$ is a solution and there are infinitely many integral solutions, then up to permutations $(a,b)=(1,1),(1,2),(2,3).$ I have found a presentation by Waldschmidt (https://webusers.imj-prg.fr/~michel.waldschmidt/articles/pdf/MarkoffEn.pdf). I would like to ask about a standard reference related to this result.

Consider the equation $x^2+ay^2+bz^2=(1+a+b)xyz.$ If $(1,1,1)$ is a solution and there are infinitely many integral solutions, then up to permutations $(a,b)=(1,1),(1,2),(2,3).$ I have found a presentation by Waldschmidt (https://webusers.imj-prg.fr/~michel.waldschmidt/articles/pdf/MarkoffEn.pdf). I would like to ask about a standard reference related to this result.

Consider the equation $x^2+ay^2+bz^2=(1+a+b)xyz.$ If there are infinitely many integral solutions, then up to permutations $(a,b)=(1,1),(1,2),(2,3).$ I have found a presentation by Waldschmidt (https://webusers.imj-prg.fr/~michel.waldschmidt/articles/pdf/MarkoffEn.pdf). I would like to ask about a standard reference related to this result.

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castor
castor
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Reference request: Markoff type equations

Consider the equation $x^2+ay^2+bz^2=(1+a+b)xyz.$ If $(1,1,1)$ is a solution and there are infinitely many integral solutions, then up to permutations $(a,b)=(1,1),(1,2),(2,3).$ I have found a presentation by Waldschmidt (https://webusers.imj-prg.fr/~michel.waldschmidt/articles/pdf/MarkoffEn.pdf). I would like to ask about a standard reference related to this result.