[15] **viXra:1808.0635 [pdf]**
*submitted on 2018-08-30 00:59:38*

**Authors:** A.I.Somsikov

**Comments:** 3 Pages. -

The solution of the problem of irrational numbers is proposed

**Category:** Number Theory

[14] **viXra:1808.0634 [pdf]**
*submitted on 2018-08-30 01:07:48*

**Authors:** A.I.Somsikov

**Comments:** 4 Pages. -

"the physical sense" (the logical contents) of complex numbers is revealed.

**Category:** Number Theory

[13] **viXra:1808.0633 [pdf]**
*submitted on 2018-08-30 01:14:33*

**Authors:** A.I.Somsikov

**Comments:** 10 Pages. -

The sense (the logical contents) of concept of numbers is revealed. Definition of arithmetic actions is given.

**Category:** Number Theory

[12] **viXra:1808.0628 [pdf]**
*submitted on 2018-08-28 07:37:10*

**Authors:** Edgar Valdebenito

**Comments:** 4 Pages.

In this note we recall a formula for pi.The distinctive feature of these formula is that pi is expressed in terms of the Lerch Transcendent Function.

**Category:** Number Theory

[11] **viXra:1808.0567 [pdf]**
*replaced on 2018-09-05 10:25:08*

**Authors:** Julian Beauchamp

**Comments:** 6 Pages.

In the first part of this paper, we show how a^x - b^y can be expressed as a new non-standard binomial formula (to an indeterminate power, n). In the second part, by fixing n to the value of z we compare this binomial formula to the standard binomial formula for c^z to prove the Beal Conjecture.

**Category:** Number Theory

[10] **viXra:1808.0552 [pdf]**
*replaced on 2018-12-17 21:45:31*

**Authors:** Toshiro Takami

**Comments:** 5 Pages.

sqrt(48a+1)=t and sqrt(48a-23)=t
Even with sqrt (24a + 1), the prime number production equation holds.
This seemed to be based on the fact that prime numbers are also represented by (12n+1), (12n-1).
(6n+1),(6n-1) does not hold the above equation.
This is also conceivable from the fact that the interval between prime numbers appearing is estimated to be about 2 or 3 times as large as sqrt (24a + 1).

**Category:** Number Theory

[9] **viXra:1808.0531 [pdf]**
*replaced on 2018-12-18 06:57:22*

**Authors:** Toshiro Takami

**Comments:** 41 Pages.

I did proof of Goldbach conjecture.
Even numbers are supplemented with prime numbers and prime numbers.
We found that even numbers and prime numbers have regularity.
How to keep this hexagon rotate no matter how big it is.
No exception was found.

**Category:** Number Theory

[8] **viXra:1808.0509 [pdf]**
*submitted on 2018-08-21 08:06:10*

**Authors:** Timothy W. Jones

**Comments:** 4 Pages.

We introduce an unaccustomed number system, H±, and show how it can be used to prove gamma
is irrational. This number system consists of
plus and minus multiplies of the terms of the harmonic series. Using some properties of ln, this system can depict the harmonic series and
lim as n goes to infinity of ln n at the same time, giving gamma as an infinite decimal. The
harmonic series converges to infinity so negative terms are forced. As all rationals can be given in H± without negative terms, it follows that must be irrational.

**Category:** Number Theory

[7] **viXra:1808.0284 [pdf]**
*submitted on 2018-08-20 01:46:43*

**Authors:** Toshiro Takami

**Comments:** 9 Pages.

【Abstract】
I found a prime number equation. All prime numbers except 2 and 3 are expressed by the following formula.
(a = positive integer, t = prime number) For other positive integers, t is an irrational number. As an exception, This generates all prime numbers except 2 and 3, but also generates a composite number of prime numbers. The composite number of the prime has regularity.

**Category:** Number Theory

[6] **viXra:1808.0254 [pdf]**
*submitted on 2018-08-18 07:57:07*

**Authors:** Bado Idriss Olivier

**Comments:** 7 Pages.

Goldbach's famous conjecture has always fascinated eminent mathematicians. In this paper we give a rigorous proof based on a new formulation, namely, that every even integer has a primo-raduis. Our proof is mainly based on the application of Chebotarev-Artin's theorem, Mertens' formula and the Principle exclusion-inclusion of Moivre

**Category:** Number Theory

[5] **viXra:1808.0201 [pdf]**
*replaced on 2019-02-18 02:02:45*

**Authors:** Ihsan Raja Muda Nasution

**Comments:** 2 Pages.

In this paper, we find the axiomatic regularity of prime numbers.

**Category:** Number Theory

[4] **viXra:1808.0190 [pdf]**
*submitted on 2018-08-14 07:42:35*

**Authors:** Edgar Valdebenito

**Comments:** 5 Pages.

Some remarks on the integral 4.371.1 in G&R table of integrals.

**Category:** Number Theory

[3] **viXra:1808.0180 [pdf]**
*submitted on 2018-08-15 04:02:30*

**Authors:** Hajime Mashima

**Comments:** 2 Pages.

Brocard's problem was presented by Henri Brocard in 1876 and 1885.
n! + 1 = m2. The number that satisfies this is called "Brown numbers"
and three are known: (n;m) = (4; 5); (5; 11); (7:71).

**Category:** Number Theory

[2] **viXra:1808.0158 [pdf]**
*submitted on 2018-08-12 11:45:22*

**Authors:** Radomir Majkic

**Comments:** 4 Pages.

There is no cuboid with all integer edges and face diagonals.

**Category:** Number Theory

[1] **viXra:1808.0074 [pdf]**
*submitted on 2018-08-07 02:00:58*

**Authors:** Angel Isaac Cruz Escalante

**Comments:** 3 Pages.

Fermat's last theorem states there are not solutions for a^x+b^x=c^x if (a,b,c,x) are positive integers and x>2, we can consider two possible cases for Fermat's last theorem, when x=4, and x=2n+1, n is natural numbers. case x=4 was proved by Fermat, here is a proof for case x=2n+1.

**Category:** Number Theory