Number Theory

1712 Submissions

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

A New Binomial Formula for the Sum of Two Powers

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

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

Taken ABaCk by Conjecturing Out-of-Box

Authors: Arthur Shevenyonov
Comments: 17 Pages. ABC conjecture

ABC conjecture and beyond, with cross-operational linkage hinting at broader convergence
Category: Number Theory

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

The Chameleon Effect, the Binomial Theorem and Beal's Conjecture

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

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

The Last Theorem of Fermat. Correct Proof

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

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

Classify Positive Integers to Prove Collatz Conjecture by Mathematical Induction (Revised Version)

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

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

The Last Theorem of Fermat. Correct Proof (Russian)

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

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

Alternate Proof for Zeta(n>1) is Irrational

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

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

An Introduction to Multi-Dimensional Identity

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

Triviality of Twin Prime Conjecture

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

Conjecture that there is no a Square of an Odd Number to be as Well Lychrel Number

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

Conjecture that there is no a Poulet Number to be as Well Lychrel Number

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

Dark Matter or Antimatter a la Cold

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

Brief Solutions to Collatz Problem, Goldbach Conjecture and Twin Primes

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

Electromagnetic Mass Reduction Repulsion Boots

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

Blue Rib Bridge or Hiway

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

Primes Obtained Concatenating 9p-12 with P^2 Where P Prime or Poulet Number

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

Primes Obtained Concatenating 2n+4 with 2n+4 Then with N Where N=3p and P Prime

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

Primes of the Form 2^a∙2^b∙2^c + D Where a, b, c, D of the Form 6k-1

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

Primes of the Form 2^a∙2^b∙2^c D Where a, b, c, D of the Form 6k+1

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

Natural Squarefree Numbers: Statistical Properties.

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

3400 Pin Oak Rd

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

Pie in Python_Piethon

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

Frequency Topology of Encryption

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

Discovering and Proving that Pi is Irrational, 2nd Edition

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

The Goldbach Conjecture

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

千古奇冤,素数有限

Authors: Liu Ran
Comments: 6 Pages.

素数个数有限,并且找出欧几里德证明的瑕疵,并举出证据
Category: Number Theory

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

Goldbach Conjecture Proof

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

Legendre Conjecture

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

Disjunctive Sequence are Rare

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

Conjecture de Brocard et Nouvelle Conjecture

Authors: Réjean Labrie
Comments: 1 Page.

542 Place Macquet
Category: Number Theory

[3] viXra:1712.0135 [pdf] replaced on 2019-04-29 10:30:25

Beal's Conjecture as Univariate Polynomial Identity Derived from Algebraic Expansion of Powers of Binomials: Analysis and Proof

Authors: Kamal Barghout
Comments: 17 Pages. Copy right-ask permission before use

The general equation of Beal’s conjecture + = , at points where its variables are numerically equal, is identified as a univariate polynomial identity derived from algebraic expansion of powers of binomials which upon expansion and reduction to two terms produces + ≡ , where the general polynomial equation has integer solution at the intersection with the line − = 0 as a special case and satisfies Beal’s condition of perfect power terms; , , , are positive integers, > 2 and + = . This algebraic identity can be represented by the addition of two vectors in the vector space of the set of all polynomials in the form () = for ∈ ℚ as a subspace of the infinite vector space over ℚ of all polynomials with basis 1, , 2 , … with the ordinary addition of polynomials and multiplication by a scalar from ℚ, where is particular to any solution to the equation. Here we look for elements in the ℚ field where the rational number can be converted to a number in exponential form that successfully combines with the basis-element to produce perfect power terms. Accordingly, it is shown that all three monomials of the identity equation numerically produce terms of perfect powers by following the rules of exponentiation which produces integer solutions to Beal’s general equation and can be obtained by expanding the corresponding binomial identity.
Category: Number Theory

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

Proof of Goldbach's Conjecture and Twin Prime Conjecture

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

Several Treasures of the Queen of Sciences

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