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We propose an equivalent condition for the Markov triples, which wasmentioned by H. Rademacher essentially. As an application, we study thesolvability of the Diophantine equation $a^2+b^2+c^2=abcf(a,b,c)$.

An equivalent condition for the Markov triples and the Diophantine equation $a^2+b^2+c^2=abcf(a,b,c)$