[16] **viXra:1806.0423 [pdf]**
*submitted on 2018-06-27 07:50:08*

**Authors:** Victor Sorokine

**Comments:** 1 Page.

The number D=A^n+B^n-C^n < 0.

**Category:** Number Theory

[15] **viXra:1806.0422 [pdf]**
*submitted on 2018-06-27 07:51:11*

**Authors:** Victor Sorokine

**Comments:** 1 Page. Russian version

Число D=A^n+B^n-C^n < 0.

**Category:** Number Theory

[14] **viXra:1806.0420 [pdf]**
*replaced on 2018-07-03 11:51:45*

**Authors:** Andrey B. Skrypnik

**Comments:** 5 Pages.

Here is the only possible Proof of the Last Theorem of the Fermat in the requirements of the Fermat of 1637. - The theorem is proved universally for all numbers. - The theorem is proved on the apparatus of Diofont arithmetic. - The proof takes no more than two notebook pages of handwritten text. - The proof is clear to the pupil of the school. - The real meaning of Fermat's words about the margins of the book page is revealed. The secret of the Last Theorem of Fermat is discovered!

**Category:** Number Theory

[13] **viXra:1806.0375 [pdf]**
*submitted on 2018-06-26 05:08:21*

**Authors:** Andrey B. Skrypnik

**Comments:** 5 Pages.

Here is the only possible Proof of the Last Theorem of the Fermat in the requirements of the Fermat of 1637.
- The theorem is proved universally for all numbers.
- The theorem is proved on the apparatus of Diofont arithmetic.
- The proof takes no more than two notebook pages of handwritten text.
- The proof is clear to the pupil of the school.
- The real meaning of Fermat's words about the margins of the book page is revealed.
The secret of the Last Theorem of Fermat is discovered!

**Category:** Number Theory

[12] **viXra:1806.0353 [pdf]**
*submitted on 2018-06-25 02:58:27*

**Authors:** Andrei Lucian Dragoi

**Comments:** 11 Pages.

This paper presents a new conjecture on the divisor summatory function (also in relation with prime numbers), offering a much higher prediction accuracy than Dirichlet's divisor problem approach. Keywords: conjecture; divisor function; divisor summatory function; prime numbers; Dirichlet's divisor problem

**Category:** Number Theory

[11] **viXra:1806.0330 [pdf]**
*submitted on 2018-06-22 11:08:32*

**Authors:** Andrey B. Skrypnik

**Comments:** 13 Pages.

Complete solution of Queens Puzzle

**Category:** Number Theory

[10] **viXra:1806.0272 [pdf]**
*submitted on 2018-06-15 11:22:27*

**Authors:** Andrey B. Skrypnik

**Comments:** 4 Pages.

Now there is a formula for calculating all primes

**Category:** Number Theory

[9] **viXra:1806.0219 [pdf]**
*submitted on 2018-06-19 08:57:13*

**Authors:** Edgar Valdebenito

**Comments:** 2 Pages.

This note presents two integrals.

**Category:** Number Theory

[8] **viXra:1806.0175 [pdf]**
*submitted on 2018-06-12 09:19:38*

**Authors:** Yuki Yoshino

**Comments:** 13 Pages.

The number 0 has no distinction between positive and negative as -0 =+0, it is a number with special properties.
In this paper, we define a new concept of numbers that seems to be special, like 0, it's name is Ami.And I propose new axioms of real numbers extended by adding Ami to Hilbert 's real axiom.

**Category:** Number Theory

[7] **viXra:1806.0095 [pdf]**
*submitted on 2018-06-07 07:25:11*

**Authors:** Vladimir Ushakov

**Comments:** 1 Page.

The key problem of MIT (matrix individualism theory) is to find a way to fill a square matrix of size N by numbers 1 to N in such a way that no row or column or diagonal contains two equal numbers, diagonal here is any line in matrix with +-45% slope. This definition of diagonal (+-45%) refers only to 1-st order individualism, later I will give a clear definition of higher order matrix individualism as well

**Category:** Number Theory

[6] **viXra:1806.0062 [pdf]**
*submitted on 2018-06-05 08:43:10*

**Authors:** Edgar Valdebenito

**Comments:** 2 Pages.

This note presents a nontrivial identity that involve the number pi: pi=3.1415926535...

**Category:** Number Theory

[5] **viXra:1806.0061 [pdf]**
*submitted on 2018-06-05 08:46:07*

**Authors:** Edgar Valdebenito

**Comments:** 4 Pages.

This note presents some definite integrals.

**Category:** Number Theory

[4] **viXra:1806.0052 [pdf]**
*submitted on 2018-06-06 02:29:12*

**Authors:** Kunle Adegoke

**Comments:** 18 Pages.

We derive several identities for arbitrary homogeneous second order recurrence sequences with constant coefficients. The results are then applied to present a harmonized study of six well known integer sequences, namely the Fibonacci sequence, the sequence of Lucas numbers, the Jacobsthal sequence, the Jacobsthal-Lucas sequence, the Pell sequence and the Pell-Lucas sequence.

**Category:** Number Theory

[3] **viXra:1806.0051 [pdf]**
*submitted on 2018-06-06 02:32:45*

**Authors:** Kunle Adegoke

**Comments:** 9 Pages.

We derive various weighted summation identities, including binomial and double binomial identities, for Tribonacci numbers. Our results contain some previously known results as special cases.

**Category:** Number Theory

[2] **viXra:1806.0046 [pdf]**
*replaced on 2018-06-10 07:22:13*

**Authors:** Yellocord soc.

**Comments:** 3 Pages.

We construct an isomorphism between the category of Ababou constants and the category of affine bundles. We explore a special case, namely the image of the integers equipped with the distinguished Ababou constant under the isomorphism. Using our new machinery we prove that the distinguished Ababou constant is composite.

**Category:** Number Theory

[1] **viXra:1806.0022 [pdf]**
*replaced on 2018-06-04 20:47:27*

**Authors:** Prashanth R. Rao, Tirumal Rao

**Comments:** 2 Pages.

In this paper we define a novel kind of prime “p” with (m+n) digits whose first “m” digits represent a prime and the next “n” digits also represent a prime in just one possible way. These primes which we call as precious primes relate three different primes and therefore products of precious primes may allow representation of complex structures such as graphs.

**Category:** Number Theory