On congruence topologies in number fields.
On congruences in number-theory
On congruent primes and class numbers of imaginary quadratic fields
We consider the problem of determining whether a given prime p is a congruent number. We present an easily computed criterion that allows us to conclude that certain primes for which congruency was previously undecided, are in fact not congruent. As a result, we get additional information on the possible sizes of Tate-Shafarevich groups of the associated elliptic curves. We also present a related criterion for primes p such that divides the class number of the imaginary quadratic field ℚ(√-p)....
On conjectures of Minkowski and Woods for n=8
On consecutive Farey arcs
On consecutive Farey arcs II
On consecutive integer pairs with the same sum of distinct prime divisors.
On consecutive integers divisible by the number of their divisors
We prove that there are no strings of three consecutive integers each divisible by the number of its divisors, and we give an estimate for the number of positive integers n ≤ x such that each of n and n + 1 is a multiple of the number of its divisors.
On consecutive integers of the form ax², by² and cz²
On Consecutive k'th Power Residues.
On constant-weight TSP-tours
Is it possible to label the edges of Kₙ with distinct integer weights so that every Hamilton cycle has the same total weight? We give a local condition characterizing the labellings that witness this question's perhaps surprising affirmative answer. More generally, we address the question that arises when "Hamilton cycle" is replaced by "k-factor" for nonnegative integers k. Such edge-labellings are in correspondence with certain vertex-labellings, and the link allows us to determine (up to a constant...
On continued fractions and diophantine approximation in power series fields
On Continued Fractions and Finite Automata.
On continuous self-maps and homeomorphisms of the Golomb space
The Golomb space is the set of positive integers endowed with the topology generated by the base consisting of arithmetic progressions with coprime . We prove that the Golomb space has continuum many continuous self-maps, contains a countable disjoint family of infinite closed connected subsets, the set of prime numbers is a dense metrizable subspace of , and each homeomorphism of has the following properties: , , , and for all . Here and denotes the set of prime divisors...
On Convex Bodies that Permit Packings of High Density.
On coset coverings of solutions of homogeneous cubic equations over finite fields.
On cosine polynomials corresponding to sets of integers
On counterexamples to local-global divisibility in commutative algebraic groups
On covering systems on rings
On coverings of almost Dedekind domains