1 citations · 1 across the 7 of their papers we have counts for
7 papers · 1 filter
Metaconjugation and Quadratic Forms
Adriana Cardoso, António Leite, António Machiavelo +2
We present a quaternionic proof that the quadratic form represents all positive integers, and that the form represents all natural numbers…
The Dedekind-Hasse Criterion in Quaternion Algebras
Adriana Cardoso, António Machiavelo
We show that a criterion for an integral domain to be a principal ideal domain (PID), due to Dedekind and Hasse, can also be applied in quaternion orders, and that it can be used t…
On the Cycle Structure of the Metacommutation Map
António Leite, António Machiavelo
Cohn and Kumar showed that the permutation on the set of the classes of left associated Hurwitz primes above an odd prime induced through metacommutation by a Hurwitz prime …
Report on Zhi-Wei Sun's "1-3-5 conjecture" and some of its refinements
António Machiavelo, Rogério Reis, Nikolaos Tsopanidis
We report here on the computational verification of a refinement of Zhi-Wei Sun's "1-3-5 conjecture" for all natural numbers up to 105 103 560 126. This, together with a result of…
Zhi-Wei Sun's 1-3-5 Conjecture and Variations
António Machiavelo, Nikolaos Tsopanidis
In this paper, using quaternion arithmetic in the ring of Lipschitz integers, we present a proof of Zhì-Wěi Sūn's "1-3-5 conjecture" for integral solutions, and for all natural num…
Dynamics of a quasi-quadratic map
Assis Azevedo, Maria Carvalho, António Machiavelo
We consider the map X defined on the rational numbers given by x --> x * ceil(x), where ceil(x) denotes the smallest integer greater than or equal to x, and study the problem of fi…
Some Connections Between The Arithmetic and The Geometry of Lipschitz Integers
António Machiavelo, Luís Roçadas
Some relationships between the arithmetic and the geometry of Lipschitz and Hurwitz integers are presented. In particular, it is shown that the (ternary) vector product of a Lipsch…