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

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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