Number Theory

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Recent submissions

Any replacements are listed further down

[1078] viXra:1602.0135 [pdf] submitted on 2016-02-12 06:32:08

The Unique Invariant Identity and Unique Consequences.

Authors: Reuven Tint
Comments: 30 Pages. Original written Russian

Received and given the unique invariant identity on a set of arbitrary numerical systems,super concise proof of Fermat's Last Theorem, another version of the Beal Conjecture solution.
Category: Number Theory

[1077] viXra:1602.0133 [pdf] submitted on 2016-02-11 21:56:29

Proof of Beal Conjecture

Authors: G.L.W.A Jayathilaka
Comments: 1 Page. This is the first real proof for beal conjecture.K can be there for any right angle triangle due to proportionality.

This is the proof of beal conjecture done by G.L.W.A Jayathilaka from Srilanka. See that K should be there for any right angle triangle due to proportionality.
Category: Number Theory

[1076] viXra:1602.0100 [pdf] submitted on 2016-02-09 03:46:24

Dark Energy Pulsating Hypothesis Proves the Riemann Hypothesis.

Authors: Terubumi Honjou
Comments: 10 Pages.

Catalogue Theoretical physics. Chapter1. Current conditionsand issues. Chapter 2 principle of particle oscillation Chapter 3 principle of pulsating for dark energy Chapter 4 4-dimensional space found Chapter 5. Solve the mystery of the dark matter discovered Chapter 6. Solve the mystery of the double slit experiment
Category: Number Theory

[1075] viXra:1602.0096 [pdf] submitted on 2016-02-08 12:01:30

Dark Energy Hypothesis Proves the Riemann Hypothesis.

Authors: Terubumi Honjou
Comments: 10 Pages.

Dark energy hypothesis proves the Riemann hypothesis. [1]. And math's biggest challenge, prove the Riemann hypothesis. [2]. Tackle the difficult Riemann hypothesis have been rejecting geniuses challenge for 150 years. [3]. The biggest challenge Prime mystery, history of mathematics, Riemann proved challenging. [4]. A new interpretation of the Riemann hypothesis. Zero point is all crosses the line. [5]. Elementary pulsation principle opens the doors of Lehman expected certification.
Category: Number Theory

[1074] viXra:1602.0065 [pdf] submitted on 2016-02-05 14:44:44

Another Bold Conjecture on Fermat Pseudoprimes

Authors: Marius Coman
Comments: 2 Pages.

In my previous paper “Bold conjecture on Fermat pseudoprimes” I stated that there exist a method to place almost any Fermat pseudoprime to base two (Poulet number) in an infinite subsequence of such numbers, defined by a quadratic polynomial, as a further term or as a starting term of such a sequence. In this paper I conjecture that there is yet another way to place a Poulet number in such a sequence defined by a polynomial, this time not necessarily quadratic.
Category: Number Theory

[1073] viXra:1602.0058 [pdf] submitted on 2016-02-05 08:43:58

Bold Conjecture on Fermat Pseudoprimes

Authors: Marius Coman
Comments: 2 Pages.

In many of my previous papers I showed various methods, formulas and polynomials designed to generate sequences, possible infinite, of Poulet numbers or Carmichael numbers. In this paper I state that there exist a method to place almost any Fermat pseudoprime to base two (Poulet number) in such a sequence, as a further term or as a starting term.
Category: Number Theory

[1072] viXra:1602.0051 [pdf] submitted on 2016-02-04 15:34:08

A List of 15 Sequences of Poulet Numbers Based on the Multiples of the Number 6

Authors: Marius Coman
Comments: 3 Pages.

In previous papers, I presented few applications of the multiples of the number 30 in the study of Carmichael numbers, i.e. in finding possible infinite sequences of such numbers; in this paper I shall list 15 probably infinite sequences of Poulet numbers that I discovered based on the multiples of the number 6.
Category: Number Theory

[1071] viXra:1602.0023 [pdf] submitted on 2016-02-02 07:16:42

Series Representation of Power Function

Authors: Kolosov Petro
Comments: 7 Pages.

This paper presents the way to make expansion for the next form function: $y=x^n, \ \forall(x,n) \in {\mathbb{N}}$ to the numerical series. The most widely used methods to solve this problem are Newton’s Binomial Theorem and Fundamental Theorem of Calculus (that is, derivative and integral are inverse operators). The paper provides the other kind of solution, except above described theorems.
Category: Number Theory

[1070] viXra:1601.0299 [pdf] submitted on 2016-01-28 03:19:09

Proof of Syracuse-Collatz-3n+1-Conjecture

Authors: Mr Romdhane DHIFAOUI
Comments: 8 Pages.

Proof of Syracuse-Collatz-3n+1-conjecture
Category: Number Theory

[1069] viXra:1601.0296 [pdf] submitted on 2016-01-27 04:19:27

Riemann Expected Certification Challenge。

Authors: Terubumi Honjou
Comments: 15 Pages.

Currently, according to the common feeling of first class mathematician who, Lehman estimates prove key to unravel ultramicroscopic structure of vacuum space trying to complete the ultimate physical theory. Pulsation principle of particle physics is the physics of dark energy, aiming for the ultimate physical theory.
Category: Number Theory

[1068] viXra:1601.0281 [pdf] submitted on 2016-01-25 19:38:36

Riemann Hypothesis is Incorrect (Second Proof)

Authors: JinHua Fei
Comments: 18 Pages.

A few years ago, I wrote my paper [4]. In the paper [4], I use Nevanlinna's Second Main Theorem of the value distribution theory, denied the Riemann Hypothesis. In this paper, I use the analytic methods, I once again denied the Riemann Hypothesis.
Category: Number Theory

[1067] viXra:1601.0219 [pdf] submitted on 2016-01-20 15:05:30

Conjecture on an Infinity of Triplets of Primes Generated by Each 3-Poulet Number

Authors: Marius Coman
Comments: 2 Pages.

In this paper I present the following conjecture: for any 3-Poulet number (Fermat pseudoprime to base two with three prime factors) P = x*y*z is true that there exist an infinity of triplets of primes [a, b, c] such that x*a + a – x = y*b + b – y = z*c + c – z.
Category: Number Theory

[1066] viXra:1601.0214 [pdf] submitted on 2016-01-19 17:56:12

Proof of Existence of Integral Solutions (A1, A2,……,an) of the Equation A1p1m + A2p2m+……+ Anpnm =0 for Any Integer “m” Greater Than or Equal to One, for Sequence of Prime P1,p2,…,pn

Authors: Prashanth R. Rao
Comments: 1 Page.

We prove using Bezout’s identity that a1p1m + a2p2m+……+ anpnm =0 has integral solutions for a1, a2,……,an, where p1,p2,…,pn is a sequence of distinct prime and m is any integer larger than or equal to 1.
Category: Number Theory

[1065] viXra:1601.0207 [pdf] submitted on 2016-01-19 01:10:19

Interpreting the Summation Notation When the Lower Limit is Greater Than the Upper Limit

Authors: Kunle Adegoke
Comments: 4 Pages.

In interpreting the sigma notation for finite summation, it is generally assumed that the lower limit of summation is less than or equal to the upper limit. This presumption has led to certain misconceptions, especially concerning what constitutes an empty sum. This paper addresses how to construe the sigma notation when the lower limit is greater than the upper limit
Category: Number Theory

[1064] viXra:1601.0161 [pdf] submitted on 2016-01-15 03:20:47

Three Conjectures on the Numbers of the Form P(p+4n)-60n Where P and P+4n Primes

Authors: Marius Coman
Comments: 2 Pages.

In this paper I present three conjectures on the numbers of the form p*(p + 4*n) – 60*n, where p and p + 4*n are primes, more accurate a general conjecture and two particular ones, on the numbers of the form p*(p + 4) – 60 respectively p*(p + 20) - 300.
Category: Number Theory

[1063] viXra:1601.0156 [pdf] submitted on 2016-01-14 12:39:01

Two Conjectures on the Numbers of the Form 4p^4-800p^2+5 Where P is Prime

Authors: Marius Coman
Comments: 2 Pages.

In this paper I state two conjectures on the numbers of the form 4*p^4 – 800*p^2 + 5, where p is prime, i.e. that there exist an infinity of primes of such form respectively that there exist an infinity of sempiprimes q*r of such form, where r = q + 40*n, where n positive integer.
Category: Number Theory

[1062] viXra:1601.0155 [pdf] submitted on 2016-01-14 12:41:06

Conjecture on the Primes of the Form (Q+n)2^n+1 Where Q Odd Prime

Authors: Marius Coman
Comments: 3 Pages.

In this paper I first conjecture that for any non-null positive integer n there exist an infinity of primes p such that the number q = (p – 1)/2^n – n is also prime and than I conjecture that for any odd prime q there exist an infinity of positive integers n such that the number p = (q + n)*2^n + 1 is prime.
Category: Number Theory

[1061] viXra:1601.0114 [pdf] submitted on 2016-01-11 07:25:32

Fermat Last Theorem Original Proof for N>2 by a Srilankan

Authors: G.L.W.A Jayathilaka
Comments: 1 Page. This is very important to the world because This proof may be Fermat original proof because brief and easy to understand. So it matches to Fermat time.

Fermat last theorem original proof when n>2, proved by me. My name is G.L.W.A Jayathilaka. Address--Guruwattha walawwa, Meetiyagoda, Srilanka
Category: Number Theory

[1060] viXra:1601.0109 [pdf] submitted on 2016-01-11 06:48:15

Goldbach's Conjecture Proof

Authors: Angel Isaac Cruz Escalante
Comments: 1 Page.

A simple proof of Goldbach's conjecture
Category: Number Theory

[1059] viXra:1601.0053 [pdf] submitted on 2016-01-06 13:59:31

Fermat Last Theorem Original Proof by a Srilankan

Authors: G.L.W.A Jayathilaka
Comments: 1 Page. all journals are invited by the Author to consider this great proof

This proof may be the original proof of Fermat last theorem that Fermat had. Because It is not difficult and easy to understand. So this proof is very useful to the world.
Category: Number Theory

[1058] viXra:1601.0043 [pdf] submitted on 2016-01-05 18:05:23

Divide the Beal’s Conjecture into Several Parts to Prove the Beal’s Conjecture

Authors: Zhang Tianshu
Comments: 23 Pages.

In this article, we first classify A, B and C according to their respective odevity, and thereby get rid of two kinds from AX+BY=CZ. Then, affirmed the existence of AX+BY=CZ in which case A, B and C have at least a common prime factor by certain of 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 positive odd numbers after divide the inequality in four. Finally, we proved that the Beal’s conjecture does hold water via the comparison between AX+BY=CZ and AX+BY≠CZ under the given requirements.
Category: Number Theory

[1057] viXra:1601.0008 [pdf] submitted on 2016-01-02 08:47:00

The Distribution of Prime Numbers in an Interval

Authors: Jian Ye
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. This paper has been published in American Journal of Mathematics and Statistics, Vol. 5 No. 6, 2015, pp. 325-328. http://article.sapub.org/10.5923.j.ajms.20150506.01.html
Category: Number Theory

[1056] viXra:1512.0484 [pdf] submitted on 2015-12-30 05:18:01

A List of Thirty-Six Polynomials and Formulas that Generate Fermat Pseudoprimes

Authors: Marius Coman
Comments: 7 Pages.

In this paper I present a simple list of polynomials (in one or two variables) and formulas having the property that they generate Carmichael numbers or Poulet numbers, polynomials and formulas that I have discovered over time.
Category: Number Theory

[1055] viXra:1512.0473 [pdf] submitted on 2015-12-29 09:48:38

Two Conjectures on Super-Poulet Numbers with Two Respectively Three Prime Factors

Authors: Marius Coman
Comments: 3 Pages.

In this paper I make two conjectures on Super-Poulet numbers with two, respectively three prime factors.
Category: Number Theory

[1054] viXra:1512.0471 [pdf] submitted on 2015-12-29 10:39:11

Sequence of Poulet Numbers Obtained by Formula mn-N+1 Where M of the Form 270k+13

Authors: Marius Coman
Comments: 2 Pages.

In this paper we conjecture that there exist an infinity of Poulet numbers of the form m*n – n + 1, where m is of the form 270*k + 13. Incidentally, verifying this conjecture, we found results that encouraged us to issue yet another conjecture, i.e. that there exist an infinity of numbers s of the form 270*k + 13 which are semiprimes s = p*q having the property that q – p + 1 is prime or power of prime.
Category: Number Theory

[1053] viXra:1512.0470 [pdf] submitted on 2015-12-29 10:41:51

Four Conjectures on the Numbers of the Form (P+270)n-N+1 Where P and P+270 Primes

Authors: Marius Coman
Comments: 3 Pages.

In this paper we conjecture that there exist an infinity of primes, respectively squares of primes, respectively semiprimes with a certain property, respectively Poulet numbers of the form (p + 270)*n – n + 1, for any p prime greater than or equal to 7, if p + 270 is also a prime number.
Category: Number Theory

[1052] viXra:1512.0468 [pdf] submitted on 2015-12-29 09:08:19

Conjecture that States that the Square of Any Prime Can be Written in a Certain Way

Authors: Marius Coman
Comments: 2 Pages.

In this paper we conjecture that the square of any prime greater than or equal to 5 can be written in one of the following three ways: (i) p*q + q – p; (ii) p*q*r + p*q – r; (iii) p*q*r + p – q*r, where p, q and r are odd primes. Incidentally, verifying this conjecture, we found results that encouraged us to issue yet another conjecture, i.e. that the square of any prime of the form 11 + 30*k can be written as 3*p*q + p – 3*q, where p and q are odd primes.
Category: Number Theory

[1051] viXra:1512.0467 [pdf] submitted on 2015-12-29 09:09:50

Conjecture Which States that Any Carmichael Number Can be Written in a Certain Way

Authors: Marius Coman
Comments: 2 Pages.

In this paper we conjecture that any Carmichael number C can be written as C = (p + 270)*(n + 1) – n, where n non-null positive integer and p prime. Incidentally, verifying this conjecture, we found results that encouraged us to issue yet another conjecture, i.e. that there exist an infinity of Poulet numbers P2 that could be written as (P1 + n)/(n + 1) – 270, where n is non-null positive integer and P1 is also a Poulet number.
Category: Number Theory

[1050] viXra:1512.0428 [pdf] submitted on 2015-12-25 21:31:37

Fermat Last Theorem Was Proved in 1991

Authors: Chunxuan Jiang
Comments: 8 Pages.

On Oct.25,1991 without using any number theory we have proved Fermat last theorem
Category: Number Theory

Replacements of recent Submissions

[525] viXra:1601.0281 [pdf] replaced on 2016-02-06 18:03:20

Riemann Hypothesis is Incorrect (Second Proof)

Authors: JinHua Fei
Comments: 12 Pages.

A few years ago, I wrote my paper [4]. In the paper [4], I use Nevanlinna's Second Main Theorem of the value distribution theory, denied the Riemann Hypothesis. In this paper, I use the analytic methods, I once again denied the Riemann Hypothesis
Category: Number Theory

[524] viXra:1601.0214 [pdf] replaced on 2016-01-22 17:56:52

Two Proofs for the Existence of Integral Solutions (A1, A2,……,an) of the Equation a1 (P1^m) + a2 (P2^m)+……+ an (Pn^m) = 0 , for Sequence of Primes P1,p2,…,pn , and Where M is a Positive Integer

Authors: Prashanth R. Rao
Comments: 2 Pages. Pls keep both versions. Thank you.

We prove using Bezout’s identity that a1p1m + a2p2m+……+ anpnm =0 has integral solutions for a1, a2,……,an, where p1,p2,…,pn is a sequence of distinct prime and m is any positive integer.
Category: Number Theory

[523] viXra:1601.0207 [pdf] replaced on 2016-01-29 12:44:49

Interpreting the Summation Notation When the Lower Limit is Greater Than the Upper Limit

Authors: Kunle Adegoke
Comments: 6 Pages. added examples, corrected typos

In interpreting the sigma notation for finite summation, it is generally assumed that the lower limit of summation is less than or equal to the upper limit. This presumption has led to certain misconceptions, especially concerning what constitutes an empty sum. This paper addresses how to construe the sigma notation when the lower limit is greater than the upper limit
Category: Number Theory

[522] viXra:1601.0109 [pdf] replaced on 2016-01-18 21:00:12

Goldbach's Conjecture Proof

Authors: Angel Isaac Cruz Escalante
Comments: 1 Page.

A proof of Goldbach's conjecture
Category: Number Theory

[521] viXra:1601.0109 [pdf] replaced on 2016-01-12 00:06:14

Goldbach's Conjecture Proof

Authors: Angel Isaac Cruz Escalante
Comments: 1 Page.

A proof of Goldbach's conjecture
Category: Number Theory

[520] viXra:1601.0109 [pdf] replaced on 2016-01-11 13:47:29

Goldbach's Conjecture Proof

Authors: Angel Isaac Cruz Escalante
Comments: 1 Page.

A proof of Goldbach's conjecture
Category: Number Theory