This analysis explores integral points on hyperbolas related to the Frobenius conjecture, suggesting new connections to algebraic structures.
The long-standing Frobenius conjecture on the unicity of ordered solutions for the Markoff equation is translated in a very simple way into an arithmetic statement on the existence of integral points on certain hyperbolas.Some previous work of Kang and Melville can then be used for relating the problem to a statement concerning rank 2 symmetric hyperbolic Kac-Moody algebras.
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J. M. Tornero (2008) studied this question.
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