On the additive complements of the primes and sets of similar growth
On the Diophantine equation
In this study, we determine when the Diophantine equation has an infinite number of positive integer solutions and for Moreover, we give all positive integer solutions of the same equation for in terms of generalized Fibonacci sequence. Lastly, we formulate a conjecture related to the Diophantine equation .
On the greatest prime factor of for a prime p and other expressions
On the number of places of convergence for Newton’s method over number fields
Let be a polynomial of degree at least 2 with coefficients in a number field , let be a sufficiently general element of , and let be a root of . We give precise conditions under which Newton iteration, started at the point , converges -adically to the root for infinitely many places of . As a corollary we show that if is irreducible over of degree at least 3, then Newton iteration converges -adically to any given root of for infinitely many places . We also conjecture that...
On the parity of the number of multiplicative partitions
On the structure of quadratic congruential sequences.
Pisot sequences which satisfy no linear recurrence
Pisot sequences which satisfy no linear recurrence II
Primes in intervals
Primitivmengen in additiven abelschen Gruppen.
Problèmes extrémaux et combinatoires en théorie des nombres
Quadratic uniformity of the Möbius function
We prove the “Möbius and Nilsequences Conjecture” for nilsystems of step 1 and 2. This paper forms a part of our program to generalise the Hardy-Littlewood method so as to handle systems of linear equations in primes.
Remarques sur la suite engendrée par des substitutions composées
Résultats et problèmes en théorie des nombres
Results on disjoint covering systems on the ring of integers
Roots of increasing sequences.
Sequences, wedges and associated sets of complex numbers
Sequential convergences on generalized Boolean algebras
In this paper we investigate convergence structures on a generalized Boolean algebra and their relations to convergence structures on abelian lattice ordered groups.
Séries formelles et produit de Hadamard
Nous nous intéressons ici essentiellement à l’algèbre de Hadamard des séries formelles. Si des résultats importants ont été obtenus dans le cas d’une variable, il n’en est pas de même dans le cas de plusieurs variables. En effet, beaucoup de problèmes posés restent encore sans réponse. C’est le cas par exemple du problème du quotient de Hadamard, ou celui de la caractérisation des éléments de Hadamard inversibles, ou les diviseurs de zéro, ou encore le problème des multiplicateurs de certains sous-ensembles...