On the appearance of primes in linear recursive sequences.
On the Arithmetic of Special Values of L Functions.
On the arrowhead-Fibonacci numbers
In this paper, we define the arrowhead-Fibonacci numbers by using the arrowhead matrix of the characteristic polynomial of the k-step Fibonacci sequence and then we give some of their properties. Also, we study the arrowhead-Fibonacci sequence modulo m and we obtain the cyclic groups from the generating matrix of the arrowhead-Fibonacci numbers when read modulo m. Then we derive the relationships between the orders of the cyclic groups obtained and the periods of the arrowhead-Fibonacci sequence...
On the average growth of random Fibonacci sequences.
On the bases with an exact order
On the behavior of a variant of Hofstadter's -sequence.
On the central coefficients of Bell matrices.
On the class of all reciprocal bases for integers.
On the coefficients of the asymptotic expansion of .
On the Collatz conjecture
We propose two conjectures which imply the Collatz conjecture. We give a numerical evidence for the second conjecture.
On the commutator lengths of certain classes of finitely presented groups.
On the complexity of infinite sequences. (Sur la complexité des suites infinies.)
On the composite Lehmer numbers with prime indices, III
On the concentration of points on modular hyperbolas and exponential curves
On the conjectures of Rauzy and Shallit for infinite words
We show a connection between a recent conjecture of Shallit and an older conjecture of Rauzy for infinite words on a finite alphabet. More precisely we show that a Rauzy-like conjecture is equivalent to Shallit's. In passing we correct a misprint in Rauzy's conjecture.
On the critical pair theory in ℤ/pℤ
On the cycle structure of linear recurring sequences.
On the Davenport constant and group algebras
For a finite abelian group G and a splitting field K of G, let (G,K) denote the largest integer l ∈ ℕ for which there is a sequence over G such that for all . If (G) denotes the Davenport constant of G, then there is the straightforward inequality (G) - 1 ≤ (G,K). Equality holds for a variety of groups, and a conjecture of W. Gao et al. states that equality holds for all groups. We offer further groups for which equality holds, but we also give the first examples of groups G for which (G) -...
On the degree of an irreducible factor of the Bernoulli polynomials
On the degree of regularity of generalized van der Waerden triples.