REVIEW 4 cited by
Uniqueness theorem of generalized Markov numbers that are prime powers
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Uniqueness theorem of generalized Markov numbers that are prime powers
abstract
In this paper, we study positive integer solutions to a generalized form of the Markov equation, given as $x^2 + y^2 + z^2 + k(yz + zx + xy) = (3 + 3k)xyz$. This equation extends the classical Markov equation $x^2 + y^2 + z^2 = 3xyz$. We generalize the concept of Cohn triples for the classical Markov equation to the generalized Markov equations. Using this, we provide a generalization of the uniqueness theorem of Markov numbers that are prime powers.
Forward citations
Cited by 4 Pith papers
-
Generalized discrete Markov spectra
The paper constructs generalized discrete Markov spectra for the family of equations x² + y² + z² + k1 yz + k2 zx + k3 xy = (3 + k1 + k2 + k3) xyz, with each spectrum element realized as both a Lagrange constant of a ...
-
Words for generalized Markov numbers
Defines words ω_t via binary-tree recursion for each positive rational slope t; matrix evaluation of ω_t yields a Markov-monodromy matrix that encodes the generalized Markov number at t.
-
Orderings of Generalized k-Markov Numbers
Generalized k-Markov numbers grow monotonically along more random lines as k increases, supporting a k-analog of Frobenius' uniqueness conjecture.
-
Orderings of k-Markov Numbers
k-Markov numbers satisfy Aigner's conjectures on their orderings and uniqueness properties in positive integer solutions.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.