Shuhei Maruyama

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math.NT2024

SL(2,Z)-matrixizations of generalized Markov numbers

Yasuaki Gyoda, Shuhei Maruyama, Yusuke Sato

For $k \geq 0$ , a $k$ -generalized Markov number is an integer which appears in some positive integer solution to the $k$ -generalized Markov equation $x^2 + y^2 + z^2 + k(yz + zx + x…

math.NT2023

Uniqueness theorem of generalized Markov numbers that are prime powers

Yasuaki Gyoda, Shuhei Maruyama

In this paper, we study positive integer solutions to a generalized form of the Markov equation, given as $x^{2} + y^{2} + z^{2} + k (y z + z x + x y) = (3 + 3 k) x y z$ . This equation extends t…