Structure of the Markoff spectrum below √12
Richard Bumby (1976)
Acta Arithmetica
Similarity:
Richard Bumby (1976)
Acta Arithmetica
Similarity:
S.M.J. Wilson (1980)
Bulletin de la Société Mathématique de France
Similarity:
David G. Cantor (1994)
Acta Arithmetica
Similarity:
Takao Komatsu (1995)
Journal de théorie des nombres de Bordeaux
Similarity:
Mollin, R. (2001)
Serdica Mathematical Journal
Similarity:
We investigate infinite families of integral quadratic polynomials {fk (X)} k∈N and show that, for a fixed k ∈ N and arbitrary X ∈ N, the period length of the simple continued fraction expansion of √fk (X) is constant. Furthermore, we show that the period lengths of √fk (X) go to infinity with k. For each member of the families involved, we show how to determine, in an easy fashion, the fundamental unit of the underlying quadratic field. We also demonstrate how the simple continued...
P. Wojtaszczyk (1986)
Studia Mathematica
Similarity:
C. Viola (1979)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Similarity:
R. A. Mollin, A. J. Van der Poorten, H. C. Williams (1994)
Journal de théorie des nombres de Bordeaux
Similarity:
It is well known that the continued fraction expansion of readily displays the midpoint of the principal cycle of ideals, that is, the point halfway to a solution of . Here we notice that, analogously, the point halfway to a solution of can be recognised. We explain what is going on.
H. Fiedler, W. Jurkat, O. Körner (1977)
Acta Arithmetica
Similarity: