**Previous months:**

2007 - 0703(3) - 0706(2)

2008 - 0807(1) - 0809(1) - 0810(1) - 0812(2)

2009 - 0901(2) - 0904(2) - 0907(2) - 0908(4) - 0909(1) - 0910(2) - 0911(1) - 0912(3)

2010 - 1001(3) - 1002(1) - 1003(55) - 1004(50) - 1005(36) - 1006(7) - 1007(11) - 1008(16) - 1009(21) - 1010(8) - 1011(7) - 1012(13)

2011 - 1101(14) - 1102(7) - 1103(13) - 1104(3) - 1105(1) - 1106(2) - 1107(1) - 1108(2) - 1109(3) - 1110(5) - 1111(4) - 1112(4)

2012 - 1201(2) - 1202(10) - 1203(6) - 1204(8) - 1205(7) - 1206(6) - 1207(5) - 1208(5) - 1209(11) - 1210(14) - 1211(10) - 1212(4)

2013 - 1301(5) - 1302(10) - 1303(16) - 1304(15) - 1305(12) - 1306(13) - 1307(25) - 1308(11) - 1309(9) - 1310(13) - 1311(15) - 1312(21)

2014 - 1401(20) - 1402(10) - 1403(23) - 1404(10) - 1405(17) - 1406(20) - 1407(34) - 1408(52) - 1409(47) - 1410(17) - 1411(17) - 1412(18)

2015 - 1501(14) - 1502(14) - 1503(35) - 1504(23) - 1505(19) - 1506(14) - 1507(16) - 1508(15) - 1509(15) - 1510(14) - 1511(9) - 1512(27)

2016 - 1601(14) - 1602(8)

Any replacements are listed further down

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

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**Authors:** Chunxuan Jiang

**Comments:** 8 Pages.

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

**Category:** Number Theory

[525] **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

[524] **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

[523] **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

[522] **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

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

**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*

**Authors:** Angel Isaac Cruz Escalante

**Comments:** 1 Page.

A proof of Goldbach's conjecture

**Category:** Number Theory