Number Theory

1601 Submissions

[14] 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

[13] 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

[12] 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

[11] 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

[10] 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

[9] 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

[8] 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

[7] 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

[6] 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

[5] 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

[4] 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

[3] 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

[2] 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

[1] 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