Even Gap and Polignac Conjecture Proof

On the gap sequence and Gilbreath's conjecture, 2021

Motivated by Gilbreath's conjecture, we develop the notion of the gap sequence induced by any sequence of numbers. We introduce the notion of the path and associated circuits induced by an originator and study the conjecture via the notion of the trace and length of a path.

viXra, 2018

Goldbach's famous conjecture has always fascinated eminent mathematicians. In this paper we give a rigorous proof based on a new formulation, namely, that every even integer has a primo-raduis. Our proof is mainly based on the application of Chebotarev-Artin's theorem, Mertens' formula and the Principle exclusion-inclusion of Moivre

2000

We find an equivalent statement of the Poincare' Conjecture in an analytical form involving the notion of the Sobolev mappings between manifolds.

Proceedings of the American Mathematical Society, 2005

Let K be an algebraically closed field, and let R be a finitely graded K-algebra which is a domain. We show that R cannot have Gelfand-Kirillov dimension strictly between 2 and 3.

Networks, 2004

Let G be a connected graph of order n. A routing in G is a set of n(n ؊ 1) fixed paths for all ordered pairs of vertices of G. The edge-forwarding index of G, (G), is the minimum of the maximum number of paths specified by a routing passing through any edge of G taken over all routings in G, and ⌬,n is the minimum of (G) taken over all graphs of order n with maximum degree at most ⌬. To determine n؊2p؊1,n for 4p ؉ 2p/3 ؉ 1 ≤ n ≤ 6p, A. Bouabdallah and D. Sotteau proposed the following conjecture in [On the edge forwarding index problem for small graphs, Networks 23 (1993), 249 -255]. The set 3 ؋ {1, 2, . . . , (4p)/3} can be partitioned into 2p pairs plus singletons such that the set of differences of the pairs is the set 2 ؋ {1, 2, . . . , p}. This article gives a proof of this conjecture and determines that n؊2p؊1,n is equal to 5 if 4p ؉ 2p/3 ؉ 1 ≤ n ≤ 6p and to 8 if 3p ؉ p/3 ؉ 1 ≤ n ≤ 3p ؉ (3p)/5 for any p ≥ 2.

Algebraic and Geometric Topology, 2009

We prove the Kauffman-Harary Conjecture, posed in 1999: given a reduced, alternating diagram D of a knot with prime determinant p, every non-trivial Fox p-coloring of D will assign different colors to different arcs.

The Michigan Mathematical Journal, 2003

We will give a proof of the Gap Labeling Conjecture formulated by Bellissard, . It makes use of a version of Connes' index theorem for foliations which is appropriate for foliated spaces, . These arise naturally in dynamics and are likely to have further applications.

In this paper, we consider the abc conjecture. In the first part, we give the proof of the conjecture c<rad^{1.63}(abc) that constitutes the key to resolve the abc conjecture. The proof of the abc conjecture is given in the second part of the paper, supposing that the abc conjecture is false, we arrive in a contradiction.

In this paper, we consider the abc conjecture. Assuming that the conjecture c < rad^{1.63}(abc) is true, we give the proof that the abc conjecture is true.