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2015 - 1501(15) - 1502(15) - 1503(36) - 1504(23) - 1505(19) - 1506(15) - 1507(4)

Any replacements are listed further down

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

**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

[978] **viXra:1507.0013 [pdf]**
*submitted on 2015-07-02 04:54:16*

**Authors:** Kolosov Petya

**Comments:** 11 Pages. -

In this paper described some new view and properties of the power function, the main aim of the work is to enter some new ideas. Also described expansion of power function, based on done research. Expansion has like Binominal theorem view, but algorithm not same.

**Category:** Number Theory

[977] **viXra:1507.0004 [pdf]**
*submitted on 2015-07-01 00:45:24*

**Authors:** Diego Liberati

**Comments:** 1 Page.

An elementary proof of the Riemann hypothesis is offered

**Category:** Number Theory

[976] **viXra:1507.0001 [pdf]**
*submitted on 2015-07-01 00:30:41*

**Authors:** Diego Liberati

**Comments:** 1 Page.

An elementary proof to the twin prime conjecture is offered

**Category:** Number Theory

[975] **viXra:1506.0198 [pdf]**
*submitted on 2015-06-27 13:35:52*

**Authors:** Reuven Tint, Michael Tint

**Comments:** 34 Pages. Original article is written in Russian.

In the history of mathematics attempts to find common solutions in integers of Diophantine equations were unsuccessful (except iterate through numbers).In this paper, we obtain an algorithm (identity) of recurrent finding countless coprime integer solutions to equations
x^4+y^4=a^4+b^4 ,
x^4=y^4+a^4+b^4
and some arising from these extraordinary consequences.

**Category:** Number Theory

[974] **viXra:1506.0190 [pdf]**
*submitted on 2015-06-26 19:21:21*

**Authors:** Mouhcine AMRAR / BACCALAUREAT SCIENCES MATHEMATIQUES

**Comments:** 4 Pages.

This work is a study of divisibility and these criteria, in which we will give general relationships and divisibility criteria. We begin this work by answering the following question: what conditions should check the digits dialing the number to make it divisible by d? Among the most known and used criteria are the divisibility by 2, 3, 5, 11...

**Category:** Number Theory

[973] **viXra:1506.0189 [pdf]**
*submitted on 2015-06-26 19:25:11*

**Authors:** Mouhcine AMRAR

**Comments:** 4 Pages.

WE GIVE ALL ABOUT PRIME NUMBERS

**Category:** Number Theory

[972] **viXra:1506.0145 [pdf]**
*submitted on 2015-06-18 15:52:27*

**Authors:** Jaykov Foukzon

**Comments:** 48 Pages.

In this paper the important applications of the Dedekind completion *R_d in transcendental number
theory is considered. Given any analytic function of one complex variable f ∈Q[z_1,z_2, . . .],we
investigate the arithmetic nature of the values of f(z) at transcendental points e^n. Main results are: (i) the both numbers e+pi and e-pi are irrational, (ii) number e^e are transcendental.

**Category:** Number Theory

[971] **viXra:1506.0144 [pdf]**
*submitted on 2015-06-18 19:58:00*

**Authors:** Yu Zhang

**Comments:** 6 Pages.

The Goldbach theorem and the twin prime theorem are homologous.the paper from the prime origin,derived the equations of the twin prime theorem and the Goldbach theorem,and new prime number theorem.

**Category:** Number Theory

[970] **viXra:1506.0142 [pdf]**
*submitted on 2015-06-18 14:55:33*

**Authors:** Bertrand Wong

**Comments:** 9 Pages.

This paper shows why the non-trivial zeros of the Riemann zeta function ζ must always be on the critical line Re(s) = 1/2 and not anywhere else on the critical strip bounded by Re(s) = 0 and Re(s) = 1, thus affirming the validity of the Riemann hypothesis.

**Category:** Number Theory

[969] **viXra:1506.0121 [pdf]**
*submitted on 2015-06-15 15:35:17*

**Authors:** Jean Pierre Morvan

**Comments:** 16 Pages.

My first proposal for a demonstration goes back to 1997, well before the editions Faber and Faber allot a bonus of 1 million dollars to that which would show the conjecture of Goldbach. Since this date, i proposed different versions on the form,but unchanged on the bottom.
In 1742, the conjecture of Goldbach was “All even number ; writing as the sum of prime numbers”. The number 1 was regarded as a prime number.

**Category:** Number Theory

[968] **viXra:1506.0102 [pdf]**
*submitted on 2015-06-13 11:08:31*

**Authors:** Guacho Perez

**Comments:** 3 Pages.

A simple study on the Goldbach Conjecture and its links to the Prime Number Theorem and Bertrand's Postulate.

**Category:** Number Theory

[967] **viXra:1506.0082 [pdf]**
*submitted on 2015-06-11 05:02:31*

**Authors:** Ihsan Raja Muda Nasution

**Comments:** 1 Page.

In this paper, we delete the zeros of the critical line.

**Category:** Number Theory

[966] **viXra:1506.0066 [pdf]**
*submitted on 2015-06-08 07:01:07*

**Authors:** J. Yun

**Comments:** 1 page

This paper offers a concise proof of Fermat’s Last Theorem using the Euclidean algorithm.

**Category:** Number Theory

[965] **viXra:1506.0065 [pdf]**
*submitted on 2015-06-08 07:37:03*

**Authors:** V.I. Saenko

**Comments:** 7 Pages.

A perfect cuboid, i.e., a rectangular parallelepiped having integer
edges, integer face diagonals, and integer space diagonal, is proved to
be is not possible.

**Category:** Number Theory

[964] **viXra:1506.0048 [pdf]**
*submitted on 2015-06-06 05:02:36*

**Authors:** J. Yun

**Comments:** 1 Page.

This paper offers a concise proof of Beal’s conjecture using the identity.

**Category:** Number Theory

[963] **viXra:1506.0047 [pdf]**
*submitted on 2015-06-06 05:04:27*

**Authors:** J. Yun

**Comments:** 1 Page.

This paper offers a plain proof of Fermat’s Last Theorem using the cosine rule.

**Category:** Number Theory

[962] **viXra:1506.0046 [pdf]**
*submitted on 2015-06-06 05:11:43*

**Authors:** J. Yun

**Comments:** 1 Page.

This paper offers a plain proof of Beal’s conjecture using the cosine rule.

**Category:** Number Theory

[961] **viXra:1506.0041 [pdf]**
*submitted on 2015-06-05 13:47:14*

**Authors:** Jan Pavo Barukčić, Ilija Barukčić

**Comments:** 12 pages. (C)Jan Pavo Barukčić,Department of Mathematics and Computer Sciences, University of Münster, Einsteinstr. 62, 48149 Münster, Germany and Ilija Barukčić, Jever, Germany, 2014,

Today, the division of zero by zero (0/0) is a concept in philosophy, mathematics and physics without a definite solution. On this view, we are left with an inadequate and unsatisfactory situation that we are not allowed to divide zero by zero while the need to divide zero by zero (i. e. divide a tensor component which is equal to zero by another tensor component which is equal to zero) is great. A solution of the philosophically, logically, mathematically and physically far reaching problem of the division of zero by zero (0/0) is still not in sight. The aim of this contribution is to solve the problem of the division of zero by zero (0/0) while relying on Einstein's theory of special relativity. In last consequence, Einstein's theory of special relativity demands the division of zero by zero. Due to Einstein's theory of special relativity it is (0/0) = 1. As we will see, either we must accept the division of zero by zero as possible and defined or we must abandon Einstein's theory of special relativity as refuted.

**Category:** Number Theory

[960] **viXra:1505.0228 [pdf]**
*submitted on 2015-05-30 10:27:21*

**Authors:** C. A. Laforet

**Comments:** 13 Pages.

In this paper, a geometric interpretation of the expression Z_1 〖[Z_0]〗^(Z_2 ), where Z_0, Z_1, and Z_2 are complex numbers is investigated. The term real number in the context of this paper is defined as any number Z=ri^θ where r and θ are rational quantities and i^θ=e^(π/2 iθ) (the angular unit in which θ is measured is defined as the iota). It is proposed that multiplication of Z_0 by Z_1 and exponentiation of Z_0 by Z_2 do not modify the number itself but rather modify the basis in which the number is represented relative to what is referred to as the Rest Basis, which is the well-known rectangular complex plane. Equations that are functions of the magnitudes and angles of Z_0, Z_1, and Z_2 are derived that quantify the basis transformations in the general case. Finally, it is proposed that real numbers as well as the bases in which the numbers are represented can be understood as pairs of helical structures with one helix representing the angular component of the number and the other helix representing the magnitude of the number. It is shown that exponentiation by a complex number can be view as interactions between these two helices.

**Category:** Number Theory

[959] **viXra:1505.0205 [pdf]**
*submitted on 2015-05-27 08:21:06*

**Authors:** Ihsan Raja Muda Nasution

**Comments:** 2 Pages.

We diagnose the body of the critical strip. Thereby, we can extract the deterministic
location of the critical line.

**Category:** Number Theory

[958] **viXra:1505.0203 [pdf]**
*submitted on 2015-05-26 15:26:42*

**Authors:** Douadi MIHOUBI

**Comments:** 19 Pages.

Based on, the well-ordering (N,<) of the set of natural numbers N, and some basic concepts of number theory, and using the proof by contradiction and the inductive proof on N, we prove that the validity of the Goldbach's statement:
every even integer 2n > 4, with n > 2, is the sum of two primes.
This result confirms the Goldbach conjecture, which allows to inserting it as theorem in number theory.
Key Words: Well-ordering (N,<), basic concepts and theorems on number theory, the indirect and inductive proofs on natural numbers.
AMS 2010: 11AXX, 11p32, 11B37.

**Category:** Number Theory

[957] **viXra:1505.0194 [pdf]**
*submitted on 2015-05-26 10:28:26*

**Authors:** Lukas Saul

**Comments:** 5 Pages.

Some definitions and elementary theorems are given here describing tonal and nagual numbers, sets, and processes.

**Category:** Number Theory

[956] **viXra:1505.0190 [pdf]**
*submitted on 2015-05-25 16:03:43*

**Authors:** Islem Ghaffor

**Comments:** 4 Pages.

In this paper we give a new formula for the relation between counting primes and twin primes, we use in this formula the arithmetic progressions and the cardinal of the set.

**Category:** Number Theory

[955] **viXra:1505.0170 [pdf]**
*submitted on 2015-05-24 11:59:01*

**Authors:** Kyle Den Hartog, The Human Species

**Comments:** 1 Page. Please leave the second author(s) "The Human Species" on there, this is intended to give credit for all so that it cannot be legally protected by any person.

This is a method of prime number verification. It is a pattern that is formed based upon the relationship of square numbers and prime numbers.

**Category:** Number Theory

[954] **viXra:1505.0156 [pdf]**
*submitted on 2015-05-22 04:39:08*

**Authors:** Ihsan Raja Muda Nasution

**Comments:** 1 Page.

We use the axiomatic method to reduce the number of zeros on the critical line. As the result, we obtain a disproof of the Riemann hypothesis.

**Category:** Number Theory

[953] **viXra:1505.0150 [pdf]**
*submitted on 2015-05-21 05:07:12*

**Authors:** Zhang Tianshu

**Comments:** 22 Pages.

In this article, first we classify A, B and C according to their respective odevity, and thereby ret rid of two kinds from AX+BY=CZ. Then affirmed AX+BY=CZ in which case A, B and C have a common prime factor by concrete examples. After that, proved AX+BY≠CZ in which case A, B and C have not any common prime factor by the mathematical induction with the aid of the symmetric law of odd numbers after the decomposition of the inequality. Finally, we have proved that the Beal’s conjecture does hold water after the comparison between AX+BY=CZ and AX+BY≠CZ under the given requirements.

**Category:** Number Theory

[952] **viXra:1505.0144 [pdf]**
*submitted on 2015-05-20 11:30:31*

**Authors:** Marius Coman

**Comments:** 3 Pages.

The Smarandache-Coman function is the function defined on the set of non-null positive integers with values in the set of non-null positive integers in the following way: SC(n) is the least number such that SC(n)! is divisible by n + r, where r is the digital root of the number n. In other words, SC(n) = S(n + r), where S is the Smarandache function. I also state, in this paper, nine conjectures on this function which seems to be particularly interesting: beside other characteristics, it seems to have as values all the prime numbers and, more than that, they seem to appear, leaving aside the non-prime values, in natural order.

**Category:** Number Theory

[951] **viXra:1505.0119 [pdf]**
*submitted on 2015-05-16 08:20:45*

**Authors:** Marouane rhafli

**Comments:** 7 Pages.

we introduce an algorithm that generates primes included in a given interval $I=[a,b]$ , the algorithm is an optimization to the segmented sieve of eratosthenes,it finds primes up to $N$ without any repetition of multiples of primes using the equation $p^{2}_{n}. p_{j}+2p_{n}.p{j}.c=N$ with $ c\in Z^{+}$ , its time complexity is sublinear $ O(nloglog(n)-n(loglog(n))^2)$.

**Category:** Number Theory

[950] **viXra:1505.0111 [pdf]**
*submitted on 2015-05-15 03:35:38*

**Authors:** T.Nakashima

**Comments:** 2 Pages.

The equivalent condition about mobius function
of The Generalized Riemann Hypothesis.

**Category:** Number Theory

[949] **viXra:1505.0107 [pdf]**
*submitted on 2015-05-13 23:34:42*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I conjecture that there exist an infinity of positive integers m of the form 6*k + 1 such that the numbers formed by concatenation n = m081 are primes or powers of primes, respectively semiprimes p*q such that q – p + 1 is prime or power of prime.

**Category:** Number Theory

[948] **viXra:1505.0106 [pdf]**
*submitted on 2015-05-14 00:58:51*

**Authors:** Marius Coman

**Comments:** 3 Pages.

In this paper I conjecture that there exist an infinity of numbers ab formed by concatenation from a multiple of 30, a, and a square of a prime, b, which are primes or powers of primes, respectively semiprimes p*q such that q – p + 1 is prime or power of prime, respectively semiprimes p1*q1 such that q1 – p1 + 1 is semiprime p2*q2 such that q2 – p2 + 1 is prime or power of prime.

**Category:** Number Theory

[947] **viXra:1505.0104 [pdf]**
*submitted on 2015-05-13 09:53:42*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I conjecture that there exist an infinity of primes m such that the number n = m*(m + 360) – 6240 is square of prime, respectively prime, respectively semiprime p*q such that q – p + 1 is prime or square of prime, respectively semiprime p1*q1 such that q1 – p1 + 1 is a semiprime q2*p2 such that q2 – p2 + 1 is prime or square of prime.

**Category:** Number Theory

[946] **viXra:1505.0081 [pdf]**
*submitted on 2015-05-10 21:32:42*

**Authors:** Lukas Saul

**Comments:** 18 Pages. Enjoy

We are transported to the infinite hotel via processes unknown and find a way to discuss with Georg Cantor himself the cardinality of infinite sets. Using Cantor's first theorem we enumerate the numbers between zero and one, and discover that Cantor's second theorem has not been proven with the rigor we expected and the diagonalization proof fails spectacularly for certain representations. However Cantor has the last laugh. Later we visit the large but finite hotel and discover that transcendental numbers of certain classes are in fact countable, and that uncountable infinites are only created by the addition of a class of numbers or objects we describe as nagual.

**Category:** Number Theory

[945] **viXra:1505.0077 [pdf]**
*submitted on 2015-05-10 11:34:55*

**Authors:** Alexander S. Nudelman

**Comments:** 5 Pages.

In this paper we formulate an intuitive Hypothesis about a new aspect of a well known method called “Sieve of Eratosthenes” and then prove that set of natural numbers N = {1, 2, . . .} contains infinite number of pairs of twin primes.

**Category:** Number Theory

[944] **viXra:1505.0044 [pdf]**
*submitted on 2015-05-05 23:48:14*

**Authors:** DaeHyeon KANG

**Comments:** 2 Pages.

Euclid's formula is fundamental and looks briefly, but We generate the pythagorean triple by this formula is not easy. therefore, I found the new formula to get the pythagorean triple easily

**Category:** Number Theory

[943] **viXra:1505.0038 [pdf]**
*submitted on 2015-05-04 22:10:43*

**Authors:** Pratish R. Rao, Prashanth R. Rao

**Comments:** 2 Pages.

In this paper we present a potentially novel partition generating algorithm for a positive integer k= k1k2.…kn-1kn . In previous papers we used a similar strategy to derive two important known mathematical results regarding factorials and a novel strategy to partition odd composites(Refs 1-3). Here we will generalize this approach to make it widely applicable to all positive integers. We believe this strategy may be an important tool to mathematicians to attack unsolved conjectures as well to derive alternate possibly simpler proofs of established theorems.

**Category:** Number Theory

[942] **viXra:1505.0030 [pdf]**
*submitted on 2015-05-03 14:31:32*

**Authors:** Chenglian Liu

**Comments:** 7 Pages.

In 2015, Liu et al. proposed a study relationship between RSA public key cryptosystem and Goldbach's conjecture properties. They discussed the relationship between RSA and Goldbach conjecture, twin prime and Goldbach conjecture. In this paper the author will extend to introduce the relationsip among Goldbach conjecture, twin prime and Fibonacci number. Based on their contribution, the author completely lists all combinations of twin prime in Goldbach conjecture.

**Category:** Number Theory

[941] **viXra:1505.0001 [pdf]**
*submitted on 2015-05-01 00:12:18*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I make three conjectures regarding the infinity of prime terms respectively the infinity of a certain kind of semiprime terms of the sequence obtained concatenating the odd powers of the number 2 to the left respectively to the right with the digit 1.

**Category:** Number Theory

[940] **viXra:1504.0248 [pdf]**
*submitted on 2015-04-30 17:49:37*

**Authors:** Marius Coman

**Comments:** 4 Pages.

In this paper I make three conjectures regarding a certain relation between the number 4320 and the squares of primes respectively four conjectures on squares of primes involving deconcatenation.

**Category:** Number Theory

[939] **viXra:1504.0239 [pdf]**
*submitted on 2015-04-29 15:08:09*

**Authors:** Kolosov Petya

**Comments:** 7 Pages.

In this paper described some new view and properties of the power function, the main aim of the work is to enter some new ideas. Also described expansion of power function, based on done research. Expansion has like Binominal theorem view, but algorithm not same.

**Category:** Number Theory

[938] **viXra:1504.0229 [pdf]**
*submitted on 2015-04-29 03:02:32*

**Authors:** .Wenlong Du

**Comments:** 6 Pages.

This paper studies the relationship between the prime divisor and Stirling's approximation. We get prime number theorem and its corrected value. We get bound for the error of the prime number theorem. Riemann hypothesis is established.

**Category:** Number Theory

[937] **viXra:1504.0217 [pdf]**
*submitted on 2015-04-27 23:31:53*

**Authors:** Pratish R. Rao, Prashanth R. Rao

**Comments:** 3 Pages.

n! is defined as the product 1.2.3………n and it popularly represents the number of ways of seating n people on n chairs. In a previous paper we conceptualized a new way of describing n!, using sequential cuts to an imaginary circle and derived a well known result. In this paper we use the same intuitive approach but reverse the cutting strategy by starting with n-cuts to the circle. We observe that this method leads us to estimate the approximate sum of an infinite convergent series involving factorials as unity.

**Category:** Number Theory

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

**Authors:** Diego Liberati

**Comments:** 1 Page.

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

[449] **viXra:1507.0004 [pdf]**
*replaced on 2015-07-02 00:59:47*

**Authors:** Diego Liberati

**Comments:** 1 Page.

A revised version of the elementary proof proposed yesterday: now positive integers are correctly called naturals

**Category:** Number Theory

[448] **viXra:1506.0144 [pdf]**
*replaced on 2015-07-03 09:36:48*

**Authors:** Yu Zhang

**Comments:** 6 Pages.

The Goldbach theorem and the twin prime theorem are homologous.the paper from the prime origin,derived the equations of the twin prime theorem and the Goldbach theorem,and new prime number theorem.

**Category:** Number Theory

[447] **viXra:1506.0142 [pdf]**
*replaced on 2015-06-22 11:08:28*

**Authors:** Bertrand Wong

**Comments:** 9 Pages.

This paper shows why the non-trivial zeros of the Riemann zeta function ζ will always be on the critical line Re(s) = 1/2 and not anywhere else on the critical strip bounded by Re(s) = 0 and Re(s) = 1, thus affirming the validity of the Riemann hypothesis.

**Category:** Number Theory

[446] **viXra:1506.0142 [pdf]**
*replaced on 2015-06-22 01:01:38*

**Authors:** Bertrand Wong

**Comments:** 9 Pages.

This paper shows why the non-trivial zeros of the Riemann zeta function ζ must always be on the critical line Re(s) = 1/2 and not anywhere else on the critical strip bounded by Re(s) = 0 and Re(s) = 1, thus affirming the validity of the Riemann hypothesis.

**Category:** Number Theory

[445] **viXra:1506.0142 [pdf]**
*replaced on 2015-06-20 06:44:32*

**Authors:** Bertrand Wong

**Comments:** 9 Pages.

This paper shows why the non-trivial zeros of the Riemann zeta function ζ must always be on the critical line Re(s) = 1/2 and not anywhere else on the critical strip bounded by Re(s) = 0 and Re(s) = 1, thus affirming the validity of the Riemann hypothesis.

**Category:** Number Theory

[444] **viXra:1505.0205 [pdf]**
*replaced on 2015-06-01 04:09:41*

**Authors:** Ihsan Raja Muda Nasution

**Comments:** 2 Pages.

We diagnose the body of the critical strip. Thereby, we can extract the deterministic
location of the critical line.

**Category:** Number Theory

[443] **viXra:1505.0119 [pdf]**
*replaced on 2015-05-16 10:19:18*

**Authors:** Marouane Rhafli

**Comments:** 7 Pages.

we introduce an algorithm that generates primes included in a given interval $I=[a,b]$ , the algorithm is an optimization to the segmented sieve of eratosthenes,it finds primes up to $N$ without any repetition of multiples of primes using the equation $p^{2}_{n}. p_{j}+2p_{n}.p{j}.c=N$ with $ c\in Z^{+}$ , its time complexity is sublinear $ O(nloglog(n)-n(loglog(n))^2)$.

**Category:** Number Theory

[442] **viXra:1505.0111 [pdf]**
*replaced on 2015-05-15 04:55:30*

**Authors:** T.Nakashima

**Comments:** 2 Pages.

The equivalent condition about mobius function
of The Generalized Riemann Hypothesis.

**Category:** Number Theory

[441] **viXra:1505.0081 [pdf]**
*replaced on 2015-05-11 12:46:46*

**Authors:** Lukas Saul

**Comments:** 18 Pages. Minor typos fixed

We are transported to the infinite hotel via processes unknown and find a way to discuss with Georg Cantor himself the cardinality of infinite sets. Using Cantor's first theorem we enumerate the numbers between zero and one, and discover that Cantor's second theorem has not been proven with the rigor we expected and the diagonalization proof fails spectacularly for certain representations. However Cantor has the last laugh. Later we visit the large but finite hotel and discover that transcendental numbers of certain classes are in fact countable, and that uncountable infinites are only created by the addition of a class of numbers or objects we describe as nagual.

**Category:** Number Theory