Related papers: Uniquely 2-divisible Bol loops

The twin primes conjecture is a very old problem. Tacitly it is supposed that the primes it deals with are finite. In the present paper we consider three problems that are not related to finite primes but deal with infinite integers. The…

Using variational minimizing methods,we prove the existence of an odd symmetric parabolic orbit for the 2-fixed center problems with weak force type homogeneous potentials.

We construct a 2-generator recursively presented group with infinite torsion length. We also explore the construction in the context of solvable and word-hyperbolic groups.

We establish the unique solvability of a coupling problem for entire functions which arises in inverse spectral theory for singular second order ordinary differential equations/two-dimensional first order systems and is also of relevance…

In this paper, we show that each finite group $G$ containing at most $p^2$ Sylow $p$-subgroups for each odd prime number $p$, is a solvable group. In fact, we give a positive answer to the conjecture in \cite{Rob}.

The existence of nonsingular classical magnetic monopole solutions is usually understood in terms of topologically nontrivial Higgs field configurations. We show that finite energy magnetic monopole solutions also exist within a class of…

We proved recently (see \cite{lhgarasu}) the result on the title for odd prime divisors of such an $n.$ The result implies for many $n's$, more precisely, for an infinity of $n$'s with an arbitrary fixed number of prime divisors, the…

For all positive non-square integer multiplier k, there is an infinity of multiples of triangular numbers which are also triangular numbers. With a simple change of variables, these triangular numbers can be found using solutions of Pell…

In this note we construct a class of counterexamples to the "composition conjecture" concerning an infinitesimal version of the center problem for the polynomial Abel equation in the complex domain.

In this paper, we prove that every pair of sufficiently large odd integers can be represented in the form of a pair of one prime, four prime cubes and $48$ powers of $2$.

A finite transitive permutation group is elusive if it contains no derangements of prime order. These groups are closely related to a longstanding open problem in algebraic graph theory known as the Polycirculant Conjecture, which asserts…

For any $\alpha $ small, we construct infinitely many $C^{1,\alpha}$ very weak solutions to the 2-Hessian equation with prescribed boundary value. The proof relies on the convex integration method and cut-off technique.

We prove the existence of infinitely many nontrivial weak periodic solutions for a class of fractional Kirchhoff problems driven by a relativistic Schr\"odinger operator with periodic boundary conditions and involving different types of…

We give all non splitting bi-unitary perfect polynomials over the prime field of two elements, which have only Mersenne polynomials as odd irreducible divisors.

We prove that the automorphism groups of simple polarized abelian varieties of odd prime dimension over finite fields are cyclic, and give a complete list of finite groups that can be realized as such automorphism groups.

As announced in [arXiv:0908.2596], we show that the non-passive finite simple groups are among the $PSL_2(q)$ with $q-1 \ge 4$ a 2-power. [arXiv:0908.2596]: Baumeister,Stein,Stroth: On Bruck Loops of 2-power Exponent

We show that there exists a positive number $M_0$ such that for any odd $M\geq M_0$ a random group of exponent $M$ with overwhelming probability is infinite in the few relator model and in the density $d$ model for small $d$.

In this paper, we present a synthetic solution to a geometric open problem involving the radical axis of two strangely defined circumcircles. The solution encapsulates two generalizations, one of which uses a powerful projective result…

We complete the enumeration of the possible roots of the Alexander polynomial (both conventional and over finite fields) of a trigonal curve. The curves are not assumed proper or irreducible.

Let k be an algebraically closed field of characteristic zero. We show that the centre of a homologically homogeneous, finitely generated k-algebra has rational singularities. In particular if a finitely generated normal commutative…