Number Theory

1404 Submissions

[10] viXra:1404.0470 [pdf] submitted on 2014-04-27 12:37:00

The Abc Conjecture is False

Authors: Th. Guyer
Comments: 2 Pages.

A Simply Conclusion about power2
Category: Number Theory

[9] viXra:1404.0466 [pdf] replaced on 2016-08-14 22:07:07

The Idea of the Arithmetica

Authors: Hajime Mashima
Comments: 9 Pages.

About 375 years ago, Pierre de Fermat wrote the following idea to Diophan- tus's "Arithmetica". Cubum autem in duos cubos, aut quadratoquadratum in duos quadra- toquadratos, et generaliter nullam in innitum ultra quadratum potes- tatem in duos eiusdem nominis fas est dividere cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet. Later, this proposition has continued to be a presence, such as the One Ring that appeared in JRR Tolkien's "Lord of the Rings". Finally in 1994, it has been proven by Sir Andrew Wiles. However, interesting Fermat's proof is still unknown. Perhaps this is assumed to algebra category.
Category: Number Theory

[8] viXra:1404.0420 [pdf] submitted on 2014-04-18 04:14:20

Goldbach, Legendre, Brocard, Elementary Considerations on Few Conjectures.

Authors: Olivier Massot
Comments: 85 Pages.

Symmetry proves to be a useful concept when it comes to studying some conjectures in Number theory. This study (english translation of the paper 1304-0060) concentrates on three already well-known conjectures and the following one: For any given prime number p, there exists at least one prime number in each and every interval [kp,(k+1)p[, where k is a non-zero integer that is less than or equal to p.
Category: Number Theory

[7] viXra:1404.0280 [pdf] replaced on 2016-07-09 04:01:12

New Proof that the Sum of Natural Number is 1/12 of Zeta Function

Authors: K. Sugiyama
Comments: 36 Pages.

   We prove that the sum of natural numbers is -1/12 of the value of the zeta function by the new method.

   Abel calculated the sum of the divergent series by the Abel summation method. However, we cannot calculate the sum of natural numbers by the method. In this paper, we calculate the sum of the natural numbers by the extended Abel summation method.
Category: Number Theory

[6] viXra:1404.0115 [pdf] submitted on 2014-04-13 19:32:55

A Trivial But Notable Observation About a Relation Between the Twin Primes and the Number 14

Authors: Marius Coman
Comments: 2 Pages.

There are known few interesting properties which distinquish twin primes from the general set of primes, like for instance that 46% of primes smaller than 19000 are Ramanujan primes while about 78% of the lesser of twin primes smaller than 19000 are Ramanujan primes. But seems that a much more trivial observation about the lesser of twin primes escaped attention: from the first 500 numbers which are lesser in a pair of twin primes, 66 of them have the following remarkable property: the sum of their digits is equal to 14.
Category: Number Theory

[5] viXra:1404.0111 [pdf] submitted on 2014-04-14 00:35:51

A Conjecture About an Infinity of Sets of Integers, Each One Having an Infinite Number of Primes

Authors: Marius Coman
Comments: 2 Pages.

In this paper, inspired by one of my previous papers posted on Vixra, I make, considering the sum of the digits of an odd integer, a conjecture about an infinity of sets of integers, each one having an infinite number of primes and I also make, considering the sum of the digits of a prime number, two other conjectures.
Category: Number Theory

[4] viXra:1404.0098 [pdf] submitted on 2014-04-12 09:00:43

A Simple and General Proof of Beal's Conjecture

Authors: Golden Gadzirayi Nyambuya
Comments: 3 Pages. To be submitted to a Peer Reviewed Journal.

Using the same method that we used in the paper http://vixra.org/abs/1309.0154 to prove Fermat's Last Theorem in a simpler and truly marvellous way, we demonstrate that Beal's Conjecture yields -- in the simplest imaginable manner; to our effort to proving it.
Category: Number Theory

[3] viXra:1404.0085 [pdf] replaced on 2014-10-28 07:33:51

An Elementary Proof of Catalan Theorem.

Authors: Jamel Ghanouchi
Comments: 8 Pages.

We begin with Catalan equation and solve it.
Category: Number Theory

[2] viXra:1404.0031 [pdf] submitted on 2014-04-04 14:34:52

Odd Perfect Number Conjecture Proof

Authors: Idan Raman
Comments: 10 Pages.

When defining O(N) as the sum of all divisors of N including himself, it is to be proved that there is no odd number which satisfy the equation: O(N)=2N
Category: Number Theory

[1] viXra:1404.0003 [pdf] replaced on 2014-10-28 07:35:41

Real Primes Definition Via a Proof to Riemann Hypothesis

Authors: Jamel Ghanouchi
Comments: 14 Pages.

We deal with the concept of prime number together with the Riemann hypothesis and present a proof of Riemann hypothesis.
Category: Number Theory