[34] **viXra:1712.0679 [pdf]**
*submitted on 2017-12-31 06:29:29*

**Authors:** Julian Beauchamp

**Comments:** 1 Page.

In this paper, we reveal a new binomial formula that expresses the sum of, or difference between two powers, a^x \pm b^y, as a binomial expansion of a single power, z. Like the standard binomial formula it includes the normal binomial coefficients, factors and indices, but includes an additional non-standard factor. The new formula (with an upper index z) mimics a standard binomial formula (to the power z) without the value of the binomial expansion changing even when z itself changes. This has exciting implications for certain diophantine equations. This short paper simply highlights its existence.

**Category:** Number Theory

[33] **viXra:1712.0669 [pdf]**
*submitted on 2017-12-30 17:43:18*

**Authors:** Arthur Shevenyonov

**Comments:** 17 Pages. ABC conjecture

ABC conjecture and beyond, with cross-operational linkage hinting at broader convergence

**Category:** Number Theory

[32] **viXra:1712.0662 [pdf]**
*submitted on 2017-12-29 15:51:45*

**Authors:** Julian Beauchamp

**Comments:** 9 Pages.

In psychology, the Chameleon Effect describes how an animal's behaviour can adapt to, or mimic, its environment through non-conscious mimicry. In the first part of this paper, we show how $a^x - b^y$ can be expressed as a binomial expansion (with an upper index, $z$) that, like a chameleon, mimics a standard binomial formula (to the power $z$) without its own value changing even when $z$ itself changes. In the second part we will show how this leads to a proof for the Beal Conjecture. We finish by outlining how this method can be applied to a more generalised form of the equation.

**Category:** Number Theory

[31] **viXra:1712.0660 [pdf]**
*submitted on 2017-12-29 05:27:48*

**Authors:** Victor Sorokine

**Comments:** 3 Pages.

The proof is based on studying digits in the endings of different numbers in Fermat's equation.

**Category:** Number Theory

[30] **viXra:1712.0656 [pdf]**
*submitted on 2017-12-29 08:47:39*

**Authors:** Zhang Tianshu

**Comments:** 24 Pages.

Positive integers which are able to be operated to 1 by the leftwards operational rule and generating positive integers which start with 1 to operate by the rightwards operational rule are one-to-one correspondence and the same. So, we refer to the bunch of integers’ chains to apply the mathematical induction, next classify positive integers to get comparable results via operations, such that finally summarize out a proof at substep according to beforehand prepared two theorems as judgmental criteria.

**Category:** Number Theory

[29] **viXra:1712.0653 [pdf]**
*submitted on 2017-12-29 12:07:03*

**Authors:** Victor Sorokine

**Comments:** 2 Pages. Russian version

We study the digits at the end of different numbers in the Fermat's Equality, and arrive to a contradiction.

**Category:** Number Theory

[28] **viXra:1712.0641 [pdf]**
*submitted on 2017-12-28 10:19:41*

**Authors:** Timothy W. Jones

**Comments:** 2 Pages. You may need to read Visualizing Zeta(n>1) and Proving its Irrationality by the same author.

This is an alternative proof that zeta(n>1) is irrational. It uses nested intervals and Cantor's Nested Interval Theorem. It is a follow up for the article Visualizing Zeta(n>1) and Proving its Irrationality.

**Category:** Number Theory

[27] **viXra:1712.0588 [pdf]**
*submitted on 2017-12-24 11:13:39*

**Authors:** Ricardo Gil

**Comments:** 5 Pages. I will attempt any problem in any subject, just provide some background.

The objective of this paper is to show people that I am now for hire($). While many scientist and mathematicians are bound by the laws of nature and physics,I am able to look beyond the laws of nature and physics and come up with solutions for virtually every problem(See my papers).While my degrees are in education I have had a hobby of submitting unsolicited solutions to the CIA for the last 20 years for free. Whether they use the solutions of not is not relevant or if they deny it or confirm it. What is relevant is that if you have a problem and are willing to pay for a solution via paypal Im willing to solve it. Submit it to Ricardo.gil@sbcglobal.net. I ask for a fair price for a viable solution. "& Ye shall know the truth and any project is achievable in 18 mos or less."

**Category:** Number Theory

[26] **viXra:1712.0572 [pdf]**
*submitted on 2017-12-22 12:57:33*

**Authors:** J. Mitchell

**Comments:** 35 Pages.

Multi-dimensional identity refers to the many labels which describe any ‘Thing’ as it exists, meaning both its describable states of existence and whatever processes generate, connect and count across those states. It develops through and out of a base2 pattern that becomes a multi-layered function which generates, relates and counts base10 numbers.

**Category:** Number Theory

[25] **viXra:1712.0565 [pdf]**
*submitted on 2017-12-23 01:17:56*

**Authors:** Divyendu Priyadarshi

**Comments:** 1 Page. i am not a professional mathematician, so if there is some silly mistake or misconceptions , please point out.

In this small paper, I have argued very simply that "Twin Prime Conjecture" is quite obvious and there is nothing to prove. In fact, it reduces to the hypothesis that prime numbers are infinite in number if we accept the quite random pattern of occurrences of of prime numbers on number line.

**Category:** Number Theory

[24] **viXra:1712.0554 [pdf]**
*submitted on 2017-12-21 12:46:22*

**Authors:** Marius Coman

**Comments:** 3 Pages.

In this paper I make the following two conjectures: (I) There exist an infinity of squares of odd numbers n^2 such that n^2 + R(n^2), where R(n^2) is the number obtained reversing the digits of n^2, is a palindromic number; (II) There is no a square of an odd number to be as well Lychrel number. Note that a Lychrel number is a natural number that cannot form a palindrome through the iterative process of repeatedly reversing its digits and adding the resulting numbers (process sometimes called the 196-algorithm, 196 being the smallest such number) – see the sequence A023108 in OEIS.

**Category:** Number Theory

[23] **viXra:1712.0543 [pdf]**
*submitted on 2017-12-21 08:23:56*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I make the following two conjectures: (I) There exist an infinity of Poulet numbers P such that P + R(P), where R(P) is the number obtained reversing the digits of P, is a palindromic number; (II) There is no a Poulet number to be as well Lychrel number. Note that a Lychrel number is a natural number that cannot form a palindrome through the iterative process of repeatedly reversing its digits and adding the resulting numbers (process sometimes called the 196-algorithm, 196 being the smallest such number) – see the sequence A023108 in OEIS.

**Category:** Number Theory

[22] **viXra:1712.0532 [pdf]**
*submitted on 2017-12-20 16:05:37*

**Authors:** Ricardo Gil

**Comments:** 1 Page. So let it be written so let it be done by CERN or any other MADD Scientist Club !!!

The objective of this paper is to suggest that a photon can be cooled to -273 Kelvin and the photon can be slowed down around 10 m/s**2 and then a positive charge can be added to the minimally charged electron of the photon to create a positron which would be dark matter or antimatter, No Que No Carnal???

**Category:** Number Theory

[21] **viXra:1712.0488 [pdf]**
*replaced on 2018-06-27 08:44:06*

**Authors:** Mesut KAVAK

**Comments:** 5 Pages.

I published some solutions a time ago to Goldbach Conjecture, Collatz Problem and Twin Primes; but I noticed that there were some serious logic voids to explain the problems. After that I made some corrections in my another article; but still there were some mistakes. Even so, I can say it easily that here I brought exact solutions for them out by new methods back to the drawing board.

**Category:** Number Theory

[20] **viXra:1712.0483 [pdf]**
*submitted on 2017-12-16 19:45:21*

**Authors:** Ricardo Gil

**Comments:** 2 Pages. This paper is about Human performance, mass reduction through repulsion and Mathematical Physics.

The purpose of this paper is to show how these electronic mass reduction repulsion boot(similar to magnetic field disruption TR3B (https://www.youtube.com/watch?v=au4hbUm4mMo) could be used on the Talos to reduce the weight of the suit.(https://www.youtube.com/watch?v=pFmFl5eE8vc).

**Category:** Number Theory

[19] **viXra:1712.0482 [pdf]**
*submitted on 2017-12-17 02:19:30*

**Authors:** Ricardo Gil

**Comments:** 1 Page. To make a Tesla car, put one or more car batteries in the front seat and run a jumper cable to the cigarette lighter.

The purpose of this paper is to point out the Blue Rib Bridge or Highway A.K.A the Pinn Oak or Hausmann Stargate.

**Category:** Number Theory

[18] **viXra:1712.0458 [pdf]**
*submitted on 2017-12-14 09:17:53*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I make the following two conjectures: (1) There exist an infinity of primes obtained concatenating 9*p – 12 with p^2 where p is a prime (for example, such a prime is 208554289 obtained concatenating 9*233 – 12 = 2085 with 233^2 = 54289); (2) There exist an infinity of primes obtained concatenating 9*p – 12 with p^2 where p is a Poulet number (for example, such a prime is 155492989441 obtained concatenating 9*1729 – 12 = 15549 with 1729^2 = 2989441).

**Category:** Number Theory

[17] **viXra:1712.0457 [pdf]**
*submitted on 2017-12-14 09:19:56*

**Authors:** Marius Coman

**Comments:** 1 Page.

In this paper I make the following conjecture: There exist an infinity of primes obtained concatenating 2*n + 4 with 2*n + 4 then with n where n = 3*p and p is a prime; for example, such primes are 19019093 obtained concatenating 190 = 2*(3*31) + 4 with 190 then with 93 = 3*31 or 12701270633 obtained concatenating 1270 = 2*(3*211) + 4 with 1270 then with 633 = 3*211. Note that for twenty-five from the first eighty primes p are obtained primes with this method.

**Category:** Number Theory

[16] **viXra:1712.0452 [pdf]**
*submitted on 2017-12-15 03:07:11*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I make the following conjecture: For any a, b, c distinct numbers of the form 6*k – 1 there exist an infinity of numbers d of the form 6*h – 1 such that the number n = 2^a*2^b*2^c + d is prime. This is a formula that conducts often to primes and composites with very few prime factors; for instance, taking a = 5 and b = 11 are obtained seventeen primes for c and d both less than 100 (for c = 17, n is prime for six values of d up to 100: 17, 29, 35, 59, 71, 77)! Also note that for [a, b, c, d] = [59, 65, 71, 53] (all four less than or equal to 71) is obtained a prime with 59 digits!

**Category:** Number Theory

[15] **viXra:1712.0451 [pdf]**
*submitted on 2017-12-15 03:09:04*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I make the following conjecture: For any a, b, c distinct numbers of the form 6*k + 1 there exist an infinity of numbers d of the form 6*h + 1 such that the number n = 2^a*2^b*2^c - d is prime. This is a formula that conducts often to primes and composites with very few prime factors; for instance, taking a = 7 and b = 13 are obtained eighteen primes for c and d both less than 100 (for c = 19, n is prime for four values of d up to 100: 7, 19, 67, 91)! Also note that for [a, b, c, d] = [49, 55, 61, 61] (all four less than or equal to 61) is obtained a prime with 50 digits!

**Category:** Number Theory

[14] **viXra:1712.0441 [pdf]**
*submitted on 2017-12-13 11:00:55*

**Authors:** Helmut Preininger

**Comments:** 42 Pages.

n this paper we calculate for various sets X (some subsets of the natural numbers) the probability of an element a of X is also squarefree. Furthermore we calculate the probability of c is squarefree, where c=a+b, a is an element of the set X and b is an element of the set Y.

**Category:** Number Theory

[13] **viXra:1712.0421 [pdf]**
*submitted on 2017-12-12 09:31:48*

**Authors:** Ricardo Gil

**Comments:** 2 Pages. Don't worry folks I have been there on foot and in a car. Remain Calm.Have fun with it.

The purpose of this paper is to explain a Stargate or Temporal anomaly on Pin Oak Road

**Category:** Number Theory

[12] **viXra:1712.0397 [pdf]**
*submitted on 2017-12-10 06:30:48*

**Authors:** Ricardo Gil

**Comments:** 2 Pages. If your computer can handle it the sky's the limit with regards to digits.

The objective of this paper is to provide everyone with a program in Piethon to be able to print 250,000 digits and if your computer allow to be able to print > 299792458 digits.

**Category:** Number Theory

[11] **viXra:1712.0396 [pdf]**
*submitted on 2017-12-10 10:16:41*

**Authors:** Ricardo Gil

**Comments:** 3 Pages. Mosses equals 500 in the Torah.

The objective of this paper is simplify frequency topology of encryption and lininear Graphs that can be represent in dimension 2 or greater.

**Category:** Number Theory

[10] **viXra:1712.0384 [pdf]**
*replaced on 2017-12-22 10:37:51*

**Authors:** Timothy W. Jones

**Comments:** 13 Pages. Additional clarifications and appendix added.

Ivan Niven's proof of the irrationality of pi is often cited because it is brief and uses only calculus. However it is not well motivated. Using the concept that a quadratic function with the same symmetric properties as sine should when multiplied by sine and integrated obey upper and lower bounds for the integral, a contradiction is generated for rational candidate values of pi. This simplifying concept yields a more motivated proof of the irrationality of pi and pi squared.

**Category:** Number Theory

[9] **viXra:1712.0366 [pdf]**
*submitted on 2017-12-10 01:30:48*

**Authors:** Barry Foster

**Comments:** 1 Page.

This treatment uses two simple facts and seems to confirm the Conjecture without providing an obvious method for discovering GP primes.

**Category:** Number Theory

[8] **viXra:1712.0359 [pdf]**
*replaced on 2017-12-12 02:10:44*

[7] **viXra:1712.0353 [pdf]**
*submitted on 2017-12-09 04:18:48*

**Authors:** Bado idriss olivier

**Comments:** 6 Pages.

In this paper, we are going to give the proof of the Goldbach conjecture by introducing the lemma which implies Goldbach conjecture. first of all we are going to prove that the lemma implies Goldbach conjecture and in the following we are going to prove the validity of the lemma by using Chébotarev-Artin theorem's, Mertens formula and the Principle of inclusion - exclusion of Moivre

**Category:** Number Theory

[6] **viXra:1712.0352 [pdf]**
*submitted on 2017-12-09 04:21:53*

**Authors:** Bado idriss olivier

**Comments:** 5 Pages.

In this paper, we are going to give the proof of legendre conjecture by using the Chebotarev -Artin 's theorem ,Dirichlet arithmetic theorem and the principle inclusion-exclusion of Moivre

**Category:** Number Theory

[5] **viXra:1712.0342 [pdf]**
*submitted on 2017-12-07 19:37:22*

**Authors:** F.L.B.Périat

**Comments:** 2 Pages.

Voici la démonstration que les nombres univers sont infiniment rare.

**Category:** Number Theory

[4] **viXra:1712.0202 [pdf]**
*submitted on 2017-12-06 19:30:08*

**Authors:** Réjean Labrie

**Comments:** 1 Page.

542 Place Macquet

**Category:** Number Theory

[3] **viXra:1712.0135 [pdf]**
*replaced on 2018-08-02 07:26:36*

**Authors:** Kamal Barghout

**Comments:** 10 Pages. The material in this article is copyrighted. Please obtain authorization from the author before the use of any part of the manuscript

Beal’s equation is identified as polynomial identity and therefore the variable x is considered a countable variable. The central theme to prove Beal’s conjecture here is identifying its numerical solution as a particular solution to the general polynomial identity of αx^l+βx^l=〖δx〗^l, where α,β, δ, and l>2 are positive integers. Beal’s equation can be represented by the addition of two vectors in the vector space of the set of all polynomials in the form p(x)=a〖 x〗^l for a∈ ℚ as a subspace of the infinite vector space over ℚ of all polynomials with basis 1,x,x^2,… with the ordinary addition of polynomials and multiplication by a scalar from ℚ, where l is particular to any solution to Beal’s equation. Accordingly, all three monomials of Beal’s equation numerically produce terms of single power by following the rules of exponentiation. Here we look for elements in the ℚ field where the rational number can be converted to a number in exponential form that successfully combine with the basis-element〖 x〗^l.

**Category:** Number Theory

[2] **viXra:1712.0098 [pdf]**
*submitted on 2017-12-05 06:02:16*

**Authors:** Choe Ryujin

**Comments:** 6 Pages.

Proof of Goldbach's conjecture and twin prime conjecture

**Category:** Number Theory

[1] **viXra:1712.0073 [pdf]**
*replaced on 2018-09-07 23:25:52*

**Authors:** Leszek W. Guła

**Comments:** 4 Pages.

Theorem about the primitive Pythagorean triple. The proper proof of the Fermat’s Last Theorem (FLT). The proof of the Goldbach’s Conjecture.

**Category:** Number Theory