O řadách s nezápornými členy
On a certain class of arithmetic functions
A homothetic arithmetic function of ratio is a function such that for every . Periodic arithmetic funtions are always homothetic, while the converse is not true in general. In this paper we study homothetic and periodic arithmetic functions. In particular we give an upper bound for the number of elements of in terms of the period and the ratio of .
On a problem of Diophantus
On a problem of Erdös and Graham.
On a problem of R.L.Graham
On a theorem of Erdös and Fuchs
On covering systems on rings
On exactly covering systems of congruences having moduli occurring at most twice
On guessing whether a sequence has a certain property.
On integers with many small prime factors
On m times covering systems of congruences
On pseudoprimes having special forms and a solution of K. Szymiczek’s problem
We use the properties of -adic integrals and measures to obtain general congruences for Genocchi numbers and polynomials and tangent coefficients. These congruences are analogues of the usual Kummer congruences for Bernoulli numbers, generalize known congruences for Genocchi numbers, and provide new congruences systems for Genocchi polynomials and tangent coefficients.
On sequences of ±1's defined by binary patterns [Book]
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.