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Generalized Cullen Numbers are positive integers of the form Cb(n) := nb n + 1. In this work we generalize some known divisibility properties of Cullen Numbers and present two primality tests for this family of integers. The first test is based in the following property of primes from this family: nb n ≡ (−1)b (mod nbn +1). It is stronger and has less… (More)

- J. M. Grau, Antonio M. Oller-Marcén, Daniel Sadornil
- Math. Comput.
- 2015

- Jorge Mart́ın-Morales, Antonio M. Oller-Marcén
- 2008

Let us consider the group G = 〈x, y | x = yn〉 with m and n nonzero integers. In this paper, we study the variety of representations R(G) and the character variety X(G) in SL(2,C) of the group G, obtaining by elementary methods an explicit primary decomposition of the ideal corresponding to X(G) in the coordinates X = tx, Y = ty and Z = txy. As an easy… (More)

Let us consider the group G = 〈x, y | xm = yn〉 with m and n nonzero integers. The set R(G) of representations of G over SL(2, C) is a four-dimensional algebraic variety which is an invariant of G. In this paper the number of irreducible components of R(G) together with their dimensions are computed. We also study the set of metabelian representations of… (More)

Let us denote by Zb(n) the number of trailing zeroes in the base b expansión of n!. In this paper we study with some detail the behavior of the function Zb. In particular, since Zb is non-decreasing, we will characterize the points where it increases and we will compute the amplitude of the jump in each of such points. In passing, we will study some… (More)

Let Zb(n) denote the number of trailing zeroes in the base-b expansion of n!. In this paper we study the connection between the expression of θ(b) := limn→∞ Zb(n)/n in base b, and that of Zb(b ). In particular, if b is a prime power, we will show the equality between the k digits of Zb(b ) and the first k digits in the fractional part of θ(b). In the… (More)

In this paper we present a way to count the number of trains that we can construct with a given set of domino pieces. As an application we obtain a new method to compute the total number of eulerian paths in an undirected graph as well as their starting and ending vertices. Resumen. En este art́ıculo presentamos una manera de contar el número de trenes que… (More)

- Jorge Mart́ın-Morales, Antonio M. Oller-Marcén
- 2008

Let us consider the group G = 〈x, y | x = yn〉 with m and n nonzero integers. In this paper, we study the variety of representations R(G) and the character variety X(G) in SL(2,C) of the group G, obtaining by elementary methods an explicit primary decomposition of the ideal corresponding to X(G) in the coordinates X = tx, Y = ty and Z = txy. As an easy… (More)

- J. M. Grau, Antonio M. Oller-Marcén
- Math. Comput.
- 2011

Generalized Cullen Numbers are positive integers of the form Cb(n) := nb n + 1. In this work we generalize some known divisibility properties of Cullen Numbers and present two primality tests for this family of integers. The first test is based in the following property of primes from this family: nb n ≡ (−1)b (mod nbn +1). It is stronger and has less… (More)