Neue Beweismethoden für einen Doppelsatz der Theorie der Potenzreste, sowie über die Erweiterung des Congruenzbegriffes
Nombres de racines d’un polynôme entier modulo
Nous montrons que l’ensemble des racines modulo une puissance d’un nombre premier d’un polynôme à coefficients entiers de degré est une union d’au plus progressions arithmétiques de modules assez grands. Nous en déduisons une majoration du nombre de ses racines dans un intervalle réel court.
Note on a congruence involving products of binomial coefficients.
Note on a method in elementary number theory.
Note on multiplicative functions satisfying congruence property. II.
Note on the congruences , ,
Note sur les indices à module composé et sur une table d''une nouvelle espèce de logarithmes.
O jednej sústave kongruencií. Poznámka k predchádzajúcemu článku J. Sedláčka.
O rozšíření pojmu kongruence
On a congruence by János Bolyai, connected with pseudoprimes.
On a congruence for the number of finite marked topologies
On a congruence of Emma Lehmer related to Euler numbers
A congruence of Emma Lehmer (1938) for Euler numbers modulo p in terms of a certain sum of reciprocals of squares of integers was recently extended to prime power moduli by T. Cai et al. We generalize this further to arbitrary composite moduli n and characterize those n for which the sum in question vanishes modulo n (or modulo n/3 when 3|n). Primes for which play an important role, and we present some numerical results.
On a conjecture of Bruckman.
On a conjecture of Erdös
On a connection of number theory with graph theory
We assign to each positive integer a digraph whose set of vertices is and for which there is a directed edge from to if . We establish necessary and sufficient conditions for the existence of isolated fixed points. We also examine when the digraph is semiregular. Moreover, we present simple conditions for the number of components and length of cycles. Two new necessary and sufficient conditions for the compositeness of Fermat numbers are also introduced.
On a linear homogeneous congruence
The number of solutions of the congruence in the box is estimated from below in the best possible way, provided for all i,j either or or .
On a problem of D. H. Lehmer and its generalization
On a problem of P. Erdos and S. Stein
On a special congruence of Carlitz.
On a variant of the Erdős-Ginzburg-Ziv problem