9 citations · 24 across the 12 of their papers we have counts for
11 papers · 1 filter
Groups and monoids of Pythagorean triples connected to conics
Marco Abrate, Stefano Barbero, Umberto Cerruti +1
We define operations that give the set of all Pythagorean triples a structure of commutative monoid. In particular, we define these operations by using injections between integer t…
Linear divisibility sequences and Salem numbers
Marco Abrate, Stefano Barbero, Umberto Cerruti +1
We study linear divisibility sequences of order 4, providing a characterization by means of their characteristic polynomials and finding their factorization as a product of linear…
The Biharmonic mean
Marco Abrate, Stefano Barbero, Umberto Cerruti +1
We briefly describe some well-known means and their properties, focusing on the relationship with integer sequences. In particular, the harmonic numbers, deriving from the harmonic…
Polynomial sequences on quadratic curves
Marco Abrate, Stefano Barbero, Umberto Cerruti +1
In this paper we generalize the study of Matiyasevich on integer points over conics, introducing the more general concept of radical points. With this generalization we are able to…
Writing pi as sum of arctangents with linear recurrent sequences, Golden mean and Lucas numbers
Marco Abrate, Stefano Barbero, Umberto Cerruti +1
In this paper, we study the representation of pi as sum of arcotangents. In particular, we obtain new identities by using linear recurrent sequences. Moreover, we provide a method…
Colored compositions, Invert operator and elegant compositions with the "black tie"
Marco Abrate, Stefano Barbero, Umberto Cerruti +1
This paper shows how the study of colored compositions of integers reveals some unexpected and original connection with the Invert operator. The Invert operator becomes an importan…