[14] **viXra:1708.0187 [pdf]**
*submitted on 2017-08-16 12:56:13*

**Authors:** Edgar Valdebenito

**Comments:** 6 Pages.

This note presents some formulas for pi.

**Category:** Number Theory

[13] **viXra:1708.0181 [pdf]**
*submitted on 2017-08-16 06:53:04*

**Authors:** Kurmet Sultan

**Comments:** 29 pages, Written in Russian

The article presents the proof of the lonely runner conjecture.

**Category:** Number Theory

[12] **viXra:1708.0177 [pdf]**
*submitted on 2017-08-16 00:48:13*

**Authors:** Kurmet Sultan

**Comments:** 49 Pages.

The article provides with the evidence of the Collatz conjecture.

**Category:** Number Theory

[11] **viXra:1708.0158 [pdf]**
*submitted on 2017-08-14 08:00:35*

**Authors:** Faisal Amin Yassein Abdelmohssin

**Comments:** 3 Pages.

I found a pattern in the Pythagorean triples formed of the natural number12;{(12,5,13), (12,9,15), (12,16, 20), (12,35,37)}. The pattern is the decreasing value of the difference z - y for the triples such that the differences form a sequence of
the even numbers {8,6,4,2} in that order. The existence of such sequence for other natural numbers transforms the Pythagorean equation into a linear
equation in y .

**Category:** Number Theory

[10] **viXra:1708.0141 [pdf]**
*submitted on 2017-08-13 04:27:47*

**Authors:** Hervé G.

**Comments:** 4 Pages.

Yet another proof that zeta(2)=Pi^2/6

**Category:** Number Theory

[9] **viXra:1708.0114 [pdf]**
*submitted on 2017-08-10 21:43:45*

**Authors:** Joseph Dise

**Comments:** 3 Pages.

A minimum number of paired composite sums is shown for all 2N. By logical extension, it proves the existence of paired prime sums for all 2N.

**Category:** Number Theory

[8] **viXra:1708.0108 [pdf]**
*replaced on 2017-08-12 18:30:40*

**Authors:** Antoine Balan

**Comments:** 2 pages, written in french

We define here a p-adic like field, called the P-alic field. We replace in fact the ring Z by Q[X] and we show a formula of decomposition of a polynomial.

**Category:** Number Theory

[7] **viXra:1708.0103 [pdf]**
*submitted on 2017-08-09 13:24:14*

**Authors:** Joseph Dise

**Comments:** 1 Page.

6x±1 are twin primes where x=6nm±(n±m) has no solution for positive integers x, n, and m. This paper follows that definition to its conclusion.

**Category:** Number Theory

[6] **viXra:1708.0082 [pdf]**
*submitted on 2017-08-08 05:09:33*

**Authors:** François Mendzina Essomba

**Comments:** 12 Pages.

I propose new formulas for the transcendent functions that I discovered.

**Category:** Number Theory

[5] **viXra:1708.0076 [pdf]**
*submitted on 2017-08-08 07:03:16*

**Authors:** Zhang Tianshu

**Comments:** 22 Pages.

Positive integers which are able to be operated to 1 by set operational rule of the Collatz conjecture and positive integers got via operations by the operational rule versus the set operational rule are one-to-one the same, thus we refer to converse operational routes, apply the mathematical induction, next classify positive integers to prove the Collatz conjecture by substeps according to beforehand prepared two theorems concerned.

**Category:** Number Theory

[4] **viXra:1708.0063 [pdf]**
*submitted on 2017-08-06 18:22:13*

**Authors:** Mendzina Essomba Francois

**Comments:** 1 Page.

A strange formula for the calculation of the natural logarithm of any real number which I guessed almost effortlessly.
This formula has the advantage of being very efficient for the calculation of the logarithm of large numbers

**Category:** Number Theory

[3] **viXra:1708.0048 [pdf]**
*submitted on 2017-08-04 15:49:56*

**Authors:** Mendzina Essomba Francois

**Comments:** 3 Pages.

I present some formulas found for the calculation of phy. Some of these formulas accelerate the calculation of decimals and others are written as a function of e and pi by continuous fractions

**Category:** Number Theory

[2] **viXra:1708.0046 [pdf]**
*submitted on 2017-08-05 03:08:52*

**Authors:** Mendzina Essomba Francois

**Comments:** 2 Pages.

some of my many pi formulae

**Category:** Number Theory

[1] **viXra:1708.0044 [pdf]**
*submitted on 2017-08-04 11:37:00*

**Authors:** Antoine Balan

**Comments:** 6 pages, written in french

Foundations of numbers theory are reviewed and some basic definitions are studied.

**Category:** Number Theory