On prime numbers in an arithmetic progression with a prime-power difference
On prime numbers p,q and r such that pq, pr, and qr are pseudoprimes
On prime primitive roots
On prime values of reducible quadratic polynomials
It is shown that Dickson’s Conjecture about primes in linear polynomials implies that if f is a reducible quadratic polynomial with integral coefficients and non-zero discriminant then for every r there exists an integer such that the polynomial represents at least r distinct primes.
On prime-detecting sequences from Apéry's recurrence formulae for and .
On primitive 3-smooth partitions of .
On primitive divisors of Mersenne numbers
On primitive lattice points in planar domains
On primitive roots.
On products and interminate powers of sequences
On products of eigenforms
On products of singular elements
On products of special linear forms with algebraic coefficients
On prolongations of rank one discrete valuations
Let be a valued field, where is a rank one discrete valuation. Let be its ring of valuation, its maximal ideal, and an extension of , defined by a monic irreducible polynomial . Assume that factors as a product of distinct powers of monic irreducible polynomials. In this paper a condition which guarantees the existence of exactly distinct valuations of extending is given, in such a way that it generalizes the results given in the paper “Prolongations of valuations to finite...
On properties of systems of arithmetic sequences
On pseudoprime numbers of special form
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 pseudorandom binary lattices
On Pyramidal Numbers of Order 4.
On pythagorean angles