Schinzel's conjecture H and divisibility in abelian linear recurring sequences
Search for Wieferich Primes through the use of Periodic Binary Strings
The result of the distributed computing projectWieferich@Home is presented: the binary periodic numbers of bit pseudo-length j ≤ 3500 obtained by replication of a bit string of bit pseudo-length k ≤ 24 and increased by one are Wieferich primes only for the cases of 1092 or 3510.
Searching for Kaprekar's constants: algorithms and results.
Searching for large elite primes.
Selberg Formulae for Gaussian integers
Semi-Characters of the Multiplicative Semigroup of Integers Modulo
Semihappy numbers.
Sequences and series involving the sequence of composite numbers.
Sequences in power residue classes.
Sequences of generalized happy numbers with small bases.
Sequences of reducible -polynomials modulo a prime.
Sequenzen der Länge 2 von Restklassencharakteren.
Séries formelles et théorie des automates.
Sets of integers composed of few prime numbers
Sets of -expansions and the Hausdorff measure of slices through fractals
We study natural measures on sets of -expansions and on slices through self similar sets. In the setting of -expansions, these allow us to better understand the measure of maximal entropy for the random -transformation and to reinterpret a result of Lindenstrauss, Peres and Schlag in terms of equidistribution. Each of these applications is relevant to the study of Bernoulli convolutions. In the fractal setting this allows us to understand how to disintegrate Hausdorff measure by slicing, leading...
Seven octonary quadratic forms
Several inequalities about the number of positive divisors of a natural number .
Sharp elementary estimates for the sequence of primes
Short character sums with Fermat quotients
Short remark on Fibonacci-Wieferich primes
This paper has been inspired by the endeavour of a large number of mathematicians to discover a Fibonacci-Wieferich prime. An exhaustive computer search has not been successful up to the present even though there exists a conjecture that there are infinitely many such primes. This conjecture is based on the assumption that the probability that a prime is Fibonacci-Wieferich is equal to . According to our computational results and some theoretical consideratons, another form of probability can...