Number Theory

1507 Submissions

[15] viXra:1507.0202 [pdf] replaced on 2015-07-29 13:06:11

The Significance Of The Non-Trivial Zeros Of The Riemann Zeta Function

Authors: Bertrand Wong
Comments: 3 Pages.

This paper expounds the role of the non-trivial zeros of the Riemann zeta function ζ and supplements the author’s earlier papers on the Riemann hypothesis. There is a lot of mystery surrounding the non-trivial zeros.
Category: Number Theory

[14] viXra:1507.0200 [pdf] replaced on 2015-12-02 13:26:42

Conjecture de Collatz (Syracuse) Démonstration

Authors: BERKOUK Mohamed
Comments: 11 Pages.

la démonstration passe par trois étapes : 1° - l’unicité du cycle trivial 2° - la décroissance de tout N du départ 3° - l’atterrissage systématique vers le cycle trivial . la démonstration de ces trois étape implique la démonstration de la conjecture de Collatz.
Category: Number Theory

[13] viXra:1507.0197 [pdf] submitted on 2015-07-27 05:09:58

A Proof of the Goldbach Conjecture

Authors: Diego Liberati
Comments: Pages.

The so called strong form is shown to derive from the recently proved so called weak form
Category: Number Theory

[12] viXra:1507.0196 [pdf] replaced on 2017-12-10 05:14:45

Démonstrations Conjecture de C.goldbach.14

Authors: BERKOUK Mohamed
Comments: 16 Pages.

La démonstration repose essentiellement sur trois théorèmes que je vais développer par la suite , le premier dite « théorème 1 » qui définit nécessairement tout nombre premier sous forme de 6m ± 1 , ∀ m ∈ N* , et suffisamment quand m ne soit pas sous forme (6xy+x+y) ou (6xy-x-y) pour tout nombre 6m+1 , et différent de la forme (6xy-x+y) pour tout nombre 6m-1. Nous appliquerons le « théorème 2 » qui définit la primalité de 6m ± 1 sans avoir à déterminer x et y de la forme. (v. la multimorielle). Le troisième théorème dite « théorème 3 » traite de la propriété de la parité en ce qui concerne le produit puis la somme de deux nombres entiers. Enfin le « théorème 4 » évoquant le postulat de Bertrand démontré par le TFNP. Après avoir passé en revue tout les cas possibles de la somme de deux, puis de trois nombres premiers et de vérifier leurs conformité avec les deux conjectures. La démonstration de la réciproque nous a conduites par une analyse logique, tout droit à celles des deux conjectures de C.GOLDBACH....
Category: Number Theory

[11] viXra:1507.0188 [pdf] submitted on 2015-07-25 05:10:50

The Levy_ Bertrand_ Goldbach Proof

Authors: Maik Becker-Sievert
Comments: 1 Page.

Proofed Bertrands Postulate Goldbach´s Ternär and Binär Conjecture Levy´s Conjecture
Category: Number Theory

[10] viXra:1507.0176 [pdf] submitted on 2015-07-23 10:38:51

Real Multiplication Nature and Its Scaling Factors

Authors: Andrea Pignataro
Comments: 7 Pages.

The goal of this paper is to explain that the real nature of the multiplication operation is based on its scaling factors and why is a common mistake to understand the multiplication as a repeated addition.
Category: Number Theory

[9] viXra:1507.0171 [pdf] replaced on 2015-07-24 07:22:01

An Elementary Proof Of Fermat's Last Theorem

Authors: Bezaliel Anotida Joshua
Comments: 5 Pages. Submitted to a formal journal for peer-review.

In this note, we provide an elementary proof of Fermat's Last Theorem.
Category: Number Theory

[8] viXra:1507.0150 [pdf] submitted on 2015-07-20 04:45:42

A Partial Proof of Carmichael Conjecture

Authors: Neelah Deka
Comments: 4 Pages.

In this note,we shall give a partial proof of carmichael conjecture
Category: Number Theory

[7] viXra:1507.0140 [pdf] submitted on 2015-07-18 04:51:43

On the Existence of at Least One Prime Number Between 5n and 6n.

Authors: Irsen Virnoy
Comments: 3 Pages.

One of the still unsolved conjectures related to prime numbers states that for all integers n>k>1 there exists at least one prime number in the interval [kn; (k+1)n]. The case k = 1 is called Bertrand's postulate, which was proved Chebyshev in the year 1850. M. El Bachraoui proved the case k = 2 in 2006, and the case k = 2 was proved by Andy Loo in 2011. This paper gives the proof for the case when k = 5.
Category: Number Theory

[6] viXra:1507.0100 [pdf] submitted on 2015-07-14 12:28:24

Disproof the Four Counterexamples for Beal's Conjecture

Authors: Valdir Monteiro dos Santos Godoi
Comments: 1 Page. Published in Bulletin of Mathematical Sciences and Applications, Vol. 13, pp. 13-13, Oct. 2015.

Probably by mistake, was published a paper which intended give some counterexamples of the Beal’s conjecture. The four examples in that paper are wrong.
Category: Number Theory

[5] viXra:1507.0091 [pdf] submitted on 2015-07-14 03:19:52

A New Conjecture on Prime Numbers

Authors: Neelabh Deka
Comments: 1 Page. A new conjecture on prime numbers is proposed in this short note.

A new conjecture on prime numbers is proposed in this short note.
Category: Number Theory

[4] viXra:1507.0033 [pdf] replaced on 2017-09-14 14:19:52

(pk mk qk) or an Unexpected Simplicity

Authors: Ralf Wüsthofen
Comments: 1 Page. Full version under 1702.0300

This note is a summary of a detailed proof of the strong Goldbach conjecture.
Category: Number Theory

[3] viXra:1507.0021 [pdf] submitted on 2015-07-03 07:04:05

La Conjecture de Polignac-Démo.docx

Authors: BERKOUK mohamed
Comments: 1 Page.

démonstration résumée , sans détailler les théorèmes de WARING ,EUCLIDE et le théorème des nombres premiers (TNP) que j'ai utilisé pour asseoir les jalons d'une démonstration de La conjecture de POLIGNAC.
Category: Number Theory

[2] viXra:1507.0004 [pdf] replaced on 2015-07-02 09:36:07

A Proof of the Riemann Hypothesis

Authors: Diego Liberati
Comments: Pages.

Taking into account infinitesimal and iperreal concepts from Robinsons' non standard analysis the proof in the previous versions has been made more general
Category: Number Theory

[1] viXra:1507.0001 [pdf] replaced on 2015-09-04 01:23:52

There Are Infinitely Many Sextuplets of Primes

Authors: Diego Liberati
Comments: 1 Page.

A proof of the conjecture is offered, also implying that: - there are infinitely many prime quadruplets - there are infinitely many twin primes - Polignac conjecture is true for n=2 and for n=4
Category: Number Theory