# Number Theory

## 1805 Submissions

 viXra:1805.0544 [pdf] replaced on 2018-06-06 19:02:43

### 17-Golden Pattern

Authors: Zeolla Gabriel Martin
Comments: 10 Pages. The previous file was damaged

This paper develops the divisibility of the so-called Simple Primes numbers-17, the discovery of a pattern to infinity, the demonstration of the inharmonics that are 2,3,5,7,11,13,17 and the harmony of 1. The discovery of infinite harmony represented in fractal numbers and patterns. This is a family before the prime numbers. This paper develops a formula to get simple prime number-17 and simple composite number-17 The simple prime numbers-17 are known as the 19-rough numbers.
Category: Number Theory

 viXra:1805.0443 [pdf] replaced on 2018-12-27 15:58:47

### La Conjecture de Collatz

Authors: Jean Pierre Morvan

Pourquoi la conjecture de COLLATZ est vraie
Category: Number Theory

 viXra:1805.0431 [pdf] submitted on 2018-05-23 17:07:06

### Formula to Find Prime Numbers and Composite Numbers with Termination 9

Authors: Zeolla Gabriel Martín

The prime numbers greater than 5 have 4 terminations in their unit to infinity (1,3,7,9) and the composite numbers divisible by numbers greater than 3 have 5 terminations in their unit to infinity, these are (1,3,5,7,9). This paper develops an expression to calculate the prime numbers and composite numbers with ending 9.
Category: Number Theory

 viXra:1805.0408 [pdf] submitted on 2018-05-21 07:56:52

### Proofing the Collatz Conjecture by Mathematical Induction

Authors: Zhang Tianshu

In this article, the author applies the mathematical induction, classifies positive integers, and passes operations according to the operational rule, to achieve the goal that proves the Collatz conjecture finally.
Category: Number Theory

 viXra:1805.0398 [pdf] replaced on 2018-05-27 19:21:30

### An Alternative Way to Write Fermat's Equation

Authors: Chris Sloane

We discovered a way to write the equation x^n+y^n-z^n=0 first studied by Fermat, in powers of 3 other variables defined as; the sum t = x+y-z, the product (xyz) and another term r = x^2+yz-xt-t^2. Once x^n+y^n-z^n is written in powers of t, r and (xyz) we found that 3 cases of a prime factor q of x^2+yz divided t. We realized that from this alternative form of Fermat’s equation if all cases of q divided t that this would lead to a contradiction and solve Fermat’s Last Theorem. Intrigued by this, we then discover that the fourth case, q=3sp+1 also divides t when using a lemma that uniquely defines an aspect of Fermat’s equation resulting in the following theorem: If x^p +y^p -z^p =0 and suppose x,y,z are pairwise co- prime then any prime factor q of (x^2 +yz) will divide t ,where t= x+y-z
Category: Number Theory

 viXra:1805.0397 [pdf] submitted on 2018-05-21 22:55:01

### Refutation of Linear Algebra as not Bivalent © Copyright 2018 by Colin James III All Rights Reserved.

Authors: Colin James III

Linear implication, resource interpretation to avoid the frame problem, and the linear transformation property are not tautologous. In particular, Tony Hoare's 1985 vending machine example as stated below is not tautologous: "Suppose a candy bar by candy, and a dollar by $1. To state a dollar will buy one candy bar, write the implication$1 ⇒ candy. But in ordinary (classical or intuitionistic) logic, from A and A ⇒ B one can conclude A ∧ B. So, ordinary logic leads us to believe that we can buy the candy bar and keep our dollar!"
Category: Number Theory

 viXra:1805.0387 [pdf] submitted on 2018-05-22 08:41:03

### Question 464: Two Integrals

Authors: Edgar Valdebenito

This note presents two integrals involving pi.
Category: Number Theory

 viXra:1805.0362 [pdf] replaced on 2018-05-23 10:37:31

### Simulation for the UNSW Quantum Programmable Computer

Authors: Ricardo Gil
Comments: 1 Page. @warlockach

The purpose of this paper is to suggest a process to generate simulations on the UNSW Programmable Quantum Computer.
Category: Number Theory

 viXra:1805.0359 [pdf] submitted on 2018-05-19 16:12:46

### Dark Matter Device To Create A New Universe

Authors: Ricardo Gil
Comments: 1 Page. @warlockach

The purpose of this paper is to suggest a Dark Matter Device that can be set off in the Cold Spot to create a new Universe.
Category: Number Theory

 viXra:1805.0325 [pdf] submitted on 2018-05-17 18:25:22

### Demonstration Riemann's Hypothesis

Authors: Wilson Torres Ovejero

158 years ago that in the complex analysis a hypothesis was raised, which was used in principle to demonstrate a theory about prime numbers, but, without any proof; with the passing Over the years, this hypothesis has become very important, since it has multiple applications to physics, to number theory, statistics, among others In this article I present a demonstration that I consider is the one that has been dodging all this time.
Category: Number Theory

 viXra:1805.0296 [pdf] submitted on 2018-05-14 19:44:25

### Formula to Find Prime Numbers and Composite Numbers with Termination 7

Authors: Zeolla Gabriel Martín

The prime numbers greater than 5 have 4 terminations in their unit to infinity (1,3,7,9) and the composite numbers divisible by numbers greater than 3 have 5 terminations in their unit to infinity, these are (1,3,5,7,9). This paper develops an expression to calculate the prime numbers and composite numbers with ending 7.
Category: Number Theory

 viXra:1805.0276 [pdf] submitted on 2018-05-13 10:36:23

### Using Scientific Notation To Express Fermat's Last Theorem

Authors: Timothy W. Jones
Comments: 2 Pages. It seems likely this angle must have been considered by say Wiles.

A number base uses any whole number greater than one. Scientific notation can be used to express any whole number in any base. As Fermat's Last Theorem concerns whole numbers greater than one to powers of $n$, we can express it using scientific notation.
Category: Number Theory

 viXra:1805.0274 [pdf] submitted on 2018-05-13 11:03:51

### Retrocausal Computing using Optical Processors

Authors: Ricardo Gil
Comments: 12 Pages. @Warlockach @Warlockach1

The purpose of this paper is to share hardware and software that can be used in Wall Street in Retrocausal optical computing.
Category: Number Theory

 viXra:1805.0269 [pdf] replaced on 2018-05-25 01:31:15

### The Last Theorem of Fermat. the Simplest Proof

Authors: Victor Sorokine

All calculations are done with numbers in base n, a prime number greater than 2. If in the Fermat equality A^n+B^n-C^n=0, the number U=A+B-C=un^k ends by k zeroes and the factor u is not ending by digit 1, after discarding k-digit endings in the numbers A, B, C, the Fermat equality turns into an inequality, which is NOT transformed back into an equality after the restoration of k-digit endings.
Category: Number Theory

 viXra:1805.0268 [pdf] replaced on 2018-05-25 01:32:16

### Теорема Ферма. Простейшее доказательство

Authors: Victor Sorokine
Comments: 2 Pages. Russian version

Доказательство проводится в системе счисления с простым основанием n>2. Если в равенстве Ферма A^n+B^n-C^n=0 число U=A+B-C=un^k оканчивается на k нулей и его сомножитель u не оканчивается на цифру 1, то после отбрасывания k- значных окончаний в числах A, B, C равенство Ферма превращается в неравенство, которое после восстановления k-значных окончаний в равенство уже НЕ превращается.
Category: Number Theory

 viXra:1805.0259 [pdf] submitted on 2018-05-14 08:47:52

### Question 454: Integrals

Authors: Edgar Valdebenito

This note presents some definite integrals.
Category: Number Theory

 viXra:1805.0258 [pdf] submitted on 2018-05-14 08:50:54

### Question 453: an Interesting Radical

Authors: Edgar Valdebenito

This note presents some formulas related with the real root of the equation: x^11-x^10-1=0 .
Category: Number Theory

 viXra:1805.0234 [pdf] submitted on 2018-05-11 12:51:36

### Quantum Programming for 72 Qubit Quantum Computers 5194 or Greater

Authors: Ricardo Gil
Comments: 2 Pages. @WARLOCKACH

The purpose of this paper is to suggest the steps for Quantum Programming for the 72 Qubit Bristlecone Quantum Computer.
Category: Number Theory

 viXra:1805.0233 [pdf] submitted on 2018-05-11 13:36:16

### Topology of the Speed of Light

Authors: Ricardo Gil

The purpose of this paper is to show the Topology difference between Einstein and Tesla.
Category: Number Theory

 viXra:1805.0230 [pdf] replaced on 2018-11-20 16:13:25

### Solution of the Erdös-Moser Equation 1+2^p+3^p+...+(k)^p=(k+1)^p

Authors: David Stacha

The Erdös-Moser equation (EM equation), named after Paul Erdös and Leo Moser, has been studied by many number theorists throughout history since combines addition, powers and summation together. An open and very interesting conjecture of Erdös-Moser states that there is no other solution of the EM equation than trivial 1+2=3. Investigation of the properties and identities of the EM equation and ultimately prove the conjecture is the main purpose of this article.
Category: Number Theory

 viXra:1805.0229 [pdf] submitted on 2018-05-11 16:50:26

### On the Riemann Hypothesis

Authors: Bertrand Wong

This paper explicates the Riemann hypothesis and proves its validity; it explains why the non-trivial zeros of the Riemann zeta function ζ will always be on the critical line Re(s) = 1/2 and not anywhere else on the critical strip bounded by Re(s) = 0 and Re(s) = 1. Much exact calculations are presented, instead of approximations, for the sake of accuracy or precision, clarity and rigor. (N.B.: New materials have been added to the paper.)
Category: Number Theory

 viXra:1805.0207 [pdf] submitted on 2018-05-10 10:13:33

### Do You Know that the Digits Have an End?

Authors: Mohamed Ababou

The book " Do you know that the digits have an end " is a scientific book, its content is clear from its title. The first thing you will say is " we all know that the digits have an end " but you should read first, my book introduce a bunch of proofs that confirm that the numbers have an end, and the digit is the same thing as the number. The Time in its relation with the numbers is the main idea in my book. This book can change the course of the history of science, it contains the correction for a popular wrong idea that is infinity. -Mohamed Ababou-
Category: Number Theory

 viXra:1805.0204 [pdf] submitted on 2018-05-10 10:51:51

### Compactification in 26 D Matter Antimatter

Authors: Ricardo Gil
Comments: 1 Page. @WARLOCKACH

The purpose of this paper is to suggest how matter and antimatter is compactified in 26 dimensions.
Category: Number Theory

 viXra:1805.0187 [pdf] submitted on 2018-05-09 15:00:03

### Pythagoras, Ellipse & Fermat

Authors: Stefan Bereza

The paper presents an attempt to solve a 300-year-old mathematical problem with minimalistic means of high-school mathematics 1]. As introduction, the Pythagorean equation of right angle triangles a^2 + b^2 = c^2 inscribed in the semicircle is reviewed; then, in an analogue way, the equation a^3+ b^3= c^3 (and then a^n + b^n = c^n) represented by a triangle inscribed in the (vertical) ellipse with its basis c making the minor axis of the ellipse and the sides of the triangle made by the factors {a,b}. Should the inscribed triangles a^3 + b^3 = c^3(and then a^n + b^n = c^n) represent the integer equations - with {a, b, c, n} positive integers, n > 2 - their sides must be rational to each other; they must form so called integer triangles. In such triangles, the square of altitude y^2(or the altitude y) must be rational to the sides. An assumption is made that at least one of the inscribed triangles may be an integral one. A unit is derived from c by dividing it by a natural number m; if the assumption is true, the unit will measure (= divide) y^2(or y) without leaving an irrational rest behind. The value of y^2(or y) is taken from the equation of the ellipse. Conducted calculations show that y^2(or y) divided by the unit leave always an irrational rest behind incompatible with c; this proves that y^2(or y) is irrational with the basis c what excludes the existence of the assumed integral triangles and, in consequence, of the discussed integral equations.
Category: Number Theory

 viXra:1805.0185 [pdf] submitted on 2018-05-09 19:09:09

### Revisit of Carmichael 1913 Work and an Elementary Approach for Fermat’s Last Theorem of Case I

Authors: Gang Li
Comments: 13 Pages. Submitted to JNT. This is an improved version of the paper posted at http://vixra.org/abs/1706.0288

We discuss an elementary approach to prove the first case of Fermat's last theorem (FLT). The essence of the proof is to notice that $a+b+c$ is of order $N^{\alpha}$ if $a^N+b^N+c^N=0$. To prove FLT, we first show that $\alpha$ can not be $2$; we then show that $\alpha$ can not be $3$, etc. While this is is the standard method of induction, we refer to it here as the infinite ascent'' technique, in contrast to Fermat's original infinite descent'' technique. A conjecture, first noted by Ribenboim is used.
Category: Number Theory

 viXra:1805.0173 [pdf] submitted on 2018-05-08 07:52:55

### Question 452: the Number pi , Elementary Formulas

Authors: Edgar Valdebenito

This note presents some elementary formulas involving pi.
Category: Number Theory

 viXra:1805.0165 [pdf] replaced on 2018-05-12 07:52:40

### Proving Fermat's Last Theorem Using Circles

Authors: Timothy W. Jones
Comments: 2 Pages. A few clarifications.

Using circles that generate areas of positive integer values, together with the transcendence of pi, we show that x^n + y^n = z^n has no solution in positive integers for n greater than or equal to 3, Fermat's Last Theorem. It fits in a margin.
Category: Number Theory

 viXra:1805.0152 [pdf] submitted on 2018-05-07 03:22:53

### On Squarefree Values of some Univariate Polynomials.

Authors: Preininger Helmut

We consider univariate Polynomials, P(s), of the form (a1 * s + b1)*...*(ak * s + bk), where a1,..,ak,b1,..,bk are natural numbers and the variable s is squarefree. We give an algorithm to calculate, for a arbitrary s, the probability that the value of P(s) is squarefree.
Category: Number Theory

 viXra:1805.0076 [pdf] submitted on 2018-05-02 20:27:06

### Formula to Find Prime Numbers and Composite Numbers with Termination 3

Authors: Zeolla Gabriel Martín

The prime numbers greater than 5 have 4 terminations in their unit to infinity (1,3,7,9) and the composite numbers divisible by numbers greater than 3 have 5 terminations in their unit to infinity, these are (1,3,5,7,9). This paper develops an expression to calculate the prime numbers and composite numbers with ending 3.
Category: Number Theory

 viXra:1805.0042 [pdf] submitted on 2018-05-01 13:32:15

### New Primality test

Authors: Nazihkhelifa
Comments: 2 Pages. Version 1

A primality test is an algorithm for determining whether an input number is prime. Among other fields of mathematics, it is used for cryptography. Unlike integer factorization, primality tests do not generally give prime factors, only stating whether the input number is prime or not. On the next version we will prove the primality tests formula
Category: Number Theory

 viXra:1805.0032 [pdf] submitted on 2018-05-02 07:54:40

### Question 450 :Some Integrals Involving the Euler's Constant

Authors: Edgar Valdebenito