Related papers: Strong Pseudo Primes to Base 2

We prove that finite sets of real numbers satisfying $|AA| \leq |A|^{1+\epsilon}$ with sufficiently small $\epsilon > 0$ cannot have small additive bases nor can they be written as a set of sums $B+C$ with $|B|, |C| \geq 2$. The result can…

We study the class of pseudo BL-algebras whose every maximal filter is normal. We present an equational base for this class and we extend these results for the class of basic pseudo hoops with fixed strong unit.

Strong variational sufficiency is a newly proposed property, which turns out to be of great use in the convergence analysis of multiplier methods. However, what this property implies for non-polyhedral problems remains a puzzle. In this…

We study substitutive systems generated by nonprimitive substitutions and show that transitive subsystems of substitutive systems are substitutive. As an application we obtain a complete characterisation of the sets of words that can appear…

We give a general framework for uniform, constant-time one-and two-dimensional scalar multiplication algorithms for elliptic curves and Jacobians of genus 2 curves that operate by projecting to the x-line or Kummer surface, where we can…

We introduce the notion of a symmetric basis of a vector space equipped with a quadratic form, and provide a sufficient and necessary condition for the existence to such a basis. Symmetric bases are then used to study Cayley graphs of…

We present methodology for constructing exact significance tests for cross tabulated data for "difficult" composite alternative hypotheses that have no natural test statistic. We construct a test for discovering Simpson's Paradox and a…

This article studies the expressive power of finite automata recognizing sets of real numbers encoded in positional notation. We consider Muller automata as well as the restricted class of weak deterministic automata, used as symbolic set…

We consider the capability of $p$-groups of class two and odd prime exponent. The question of capability is shown to be equivalent to a statement about vector spaces and linear transformations, and using the equivalence we give proofs of…

A single parameter cubic composite test for odd positive integers is given which relies on the discriminant always being a square integer. This test has no known counterexample despite extensive verifications. As well as a comparison with…

We prove the Banach strong Novikov conjecture for groups having polynomially bounded higher-order combinatorial functions. This includes all automatic groups.

A recent heuristic argument based on basic concepts in spectral analysis showed that the twin prime conjecture and a few other related primes counting problems are valid. A rigorous version of the spectral method, and a proof of the more…

Every natural number greater than $2$ can be written as the sum of a prime and a square-free number, and recent work has imposed additional divisibility conditions on the square-free number. We overcome limitations in these works to prove…

We give a general description of the structure of a discrete double groupoid (with an extra, quite natural, filling condition) in terms of groupoid factorizations and groupoid 2-cocycles with coefficients in abelian group bundles. Our…

In the paper "An Abelian Loop for Non-Composites" (arXiv:110.14716), we introduced a group-like structure consisting of odd prime numbers and 1, with properties that allowed us to prove analogous results to well known theorems in Number…

We give elementary proofs of some congruence criteria to compute binomial coefficients in modulo a prime. These criteria are analogues to the symmetry property of binomial coefficients. We give extended version of Lucas Theorem by using…

We study hyperbolic systems with multiplicities and smo\-oth coefficients. In the case of non-analytic, smooth coefficients, we prove well-posedness in any Gevrey class and when the coefficients are analytic, we prove $C^\infty$…

In this work we use the number classification in families of the form 6n+1, and 6n+5 with n integer (Such families contain all odd prime numbers greater than 3 and other compound numbers related with primes). We will use this kind of…

We give an entirely new approach to the problem of mutually unbiased bases (MUBs), based on a Fourier analytic technique in additive combinatorics. The method provides a short and elegant generalization of the fact that there are at most…

Let $p\equiv 8\mod 9$ be a prime. In this paper we give a sufficient condition such that at least one of $p$ and $p^2$ is the sum of two rational cubes. This is the first general result on the $8$ case of the so-called Sylvester conjecture.