Number Theory

1602 Submissions

[17] viXra:1602.0359 [pdf] submitted on 2016-02-28 07:19:45

Disproof of Michiwaki’s et Al. ‘Reality of the Division by Zero Z/0 = 0’

Authors: Ilija Barukčić
Comments: 5 pages. (C) Ilija Barukčić, Jever, Germany, 2016. All rights reserved.

The law of non-contradiction (LNC) is still one of the foremost among the principles of science and equally a fundamental principle of scientific inquiry too. Without the principle of non-contradiction we could not be able to distinguish between something true and something false. There are arguably many versions of the principle of non-contradiction which can be found in literature. The method of reductio ad absurdum itself is grounded on the validity of the principle of non-contradiction. To be consistent, a claim / a theorem / a proposition / a statement et cetera accepted as correct, cannot lead to a logical contradiction. In general, a claim / a theorem / a proposition / a statement et cetera which leads to the conclusion that +1 = +0 is refuted.
Category: Number Theory

[16] viXra:1602.0346 [pdf] submitted on 2016-02-27 09:04:31

Prove Collatz Conjecture by Mathematical Induction via the Two-Way Operations (Revised Version)

Authors: Zhang Tianshu
Comments: 28 Pages.

If every positive integer is able to be operated to 1 by the set operational rule of the Collatz conjecture, then begin with 1, we can get all positive integers after make infinitely many operations on the contrary of the set operational rule. In this article, we shall prove that the Collatz conjecture by the mathematical induction via the two-way operations is tenable. Keywords: mathematical induction; the two-way operational rules; classify positive integers; the bunch of integers’ chains; operational routes
Category: Number Theory

[15] viXra:1602.0343 [pdf] submitted on 2016-02-27 06:48:52

Every Large Prime Must Lie on a Diriclet’s Arithmetic Sequence and a Simple Method to Identify Such Arithmetic Progressions

Authors: Prashanth R. Rao
Comments: 1 Page.

Dirichlet’s theorem establishes that every arithmetic progression of the form a+nb where gcd(a,b)=1 contains infinitely many primes for positive integers a and b and n=1,2,3,4,………. . We show a simple proof for the existence of such an arithmetic progression for every large prime. This also reveals a method to identify arithmetic progressions on which a particular prime will appear.
Category: Number Theory

[14] viXra:1602.0279 [pdf] submitted on 2016-02-22 04:50:56

Observation on the Period of the Rational Number P÷d + D÷P Where P is a 3-Poulet Number and D Its Least Prime Factor

Authors: Marius Coman
Comments: 2 Pages.

In this paper I make the following observation: let P be a 3-Poulet number, d its least prime factor and q one of the other two prime factors; then the length of the period of the rational number P/d + d/P is for almost any P equal to q – 1 or equal to (q – 1)/n or equal to (q – 1)*n, where n positive integer.
Category: Number Theory

[13] viXra:1602.0276 [pdf] submitted on 2016-02-22 05:51:50

Conjecture on the Period of the Rational Number P÷d + D÷P Where P is a 2-Poulet Number and D Its Least Prime Factor

Authors: Marius Coman
Comments: 2 Pages.

In this paper I state the following conjecture: let P be a 2-Poulet number, d its least prime factor and q the other one; then the length of the period of the rational number P/d + d/P is equal to (q – 1)/n, where n positive integer.
Category: Number Theory

[12] viXra:1602.0212 [pdf] submitted on 2016-02-17 12:04:25

Observation on the Numbers 4p^2+2p+1 Where P and 2p-1 Are Primes

Authors: Marius Coman
Comments: 2 Pages.

In this paper I observe that many numbers of the form 4*p^2 + 2*p + 1, where p and 2*p – 1 are odd primes, meet one of the following three conditions: (i) they are primes; (ii) they are equal to d*Q, where d is the least prime factor and Q the product of the others, and Q = (n*d – n + m)/m; (iii) they are equal to d*Q, where d is the least prime factor and Q the product of the others, and Q = (n*d + n - m)/m, and I make few related notes.
Category: Number Theory

[11] viXra:1602.0205 [pdf] submitted on 2016-02-17 05:11:25

Observation on the Numbers 4p^2-2p-1 Where P and 2p-1 Are Primes

Authors: Marius Coman
Comments: 2 Pages.

In this paper I observe that many numbers of the form 4*p^2 – 2*p – 1, where p and 2*p – 1 are odd primes, meet one of the following three conditions: (i) they are primes; (ii) they are equal to d*Q, where d is the least prime factor and Q the product of the others, and Q = n*d – n + 1; (iii) they are equal to d*Q, where d is the least prime factor and Q the product of the others, and Q = n*d + n – 1, and I make few related notes.
Category: Number Theory

[10] viXra:1602.0201 [pdf] submitted on 2016-02-17 07:07:09

Divide Beal’s Conjecture into Several Parts Gradually to Prove Beal’s Conjecture

Authors: Zhang Tianshu
Comments: 26 Pages.

In this article, we first classify A, B and C according to their respective odevity, and thereby get rid of two kinds from AX+BY=CZ. Then, affirmed the existence of AX+BY=CZ in which case A, B and C have at least a common prime factor by certain of concrete equalities. After that, proved AX+BY≠CZ in which case A, B and C have not any common prime factor by the mathematical induction with the aid of the symmetric law of positive odd numbers after divide the inequality in four. Finally, reached a conclusion that the Beal’s conjecture holds water via the comparison between AX+BY=CZ and AX+BY≠CZ under the given requirements.
Category: Number Theory

[9] viXra:1602.0200 [pdf] submitted on 2016-02-17 07:15:37

Prove Collatz Conjecture by Mathematical Induction via the Two-Way Operations

Authors: Zhang Tianshu
Comments: 29 Pages.

If every positive integer is able to be operated to 1 by the set operational rule of the Collatz conjecture, then begin with 1, we can get all positive integers after make infinitely many operations on the contrary of the set operational rule. In this article, we shall prove that the Collatz conjecture by the mathematical induction via the two-way operations is tenable.
Category: Number Theory

[8] viXra:1602.0176 [pdf] submitted on 2016-02-15 09:09:05

The Differences of More and Less in Number that Proves 1+1(P+2)

Authors: Aaron Chau
Comments: 5 Pages.

Due to the Law 1: the numbers of the odds (subtractor) are more, and Law 2: the numbers of the odd integer (difference) are less; it is stressed in this article that the odd spaces which are located at the bottom line of the prime-odd pairs will never be filled in by the numbers of the odd integer, they have to be filled in by the primes (minuend) as well. Therefore, The Differences of More and Less in Number that Proves 1+1(P+2).
Category: Number Theory

[7] viXra:1602.0135 [pdf] submitted on 2016-02-12 06:32:08

The Unique Invariant Identity and Unique Consequences.

Authors: Reuven Tint
Comments: 30 Pages. Original written Russian

Received and given the unique invariant identity on a set of arbitrary numerical systems,super concise proof of Fermat's Last Theorem, another version of the Beal Conjecture solution.
Category: Number Theory

[6] viXra:1602.0133 [pdf] submitted on 2016-02-11 21:56:29

Proof of Beal Conjecture

Authors: G.L.W.A Jayathilaka
Comments: 1 Page. This is the first real proof for beal conjecture.K can be there for any right angle triangle due to proportionality.

This is the proof of beal conjecture done by G.L.W.A Jayathilaka from Srilanka. See that K should be there for any right angle triangle due to proportionality.
Category: Number Theory

[5] viXra:1602.0100 [pdf] submitted on 2016-02-09 03:46:24

Dark Energy Pulsating Hypothesis Proves the Riemann Hypothesis.

Authors: Terubumi Honjou
Comments: 10 Pages.

Catalogue Theoretical physics. Chapter1. Current conditionsand issues. Chapter 2 principle of particle oscillation Chapter 3 principle of pulsating for dark energy Chapter 4 4-dimensional space found Chapter 5. Solve the mystery of the dark matter discovered Chapter 6. Solve the mystery of the double slit experiment
Category: Number Theory

[4] viXra:1602.0096 [pdf] submitted on 2016-02-08 12:01:30

Dark Energy Hypothesis Proves the Riemann Hypothesis.

Authors: Terubumi Honjou
Comments: 10 Pages.

Dark energy hypothesis proves the Riemann hypothesis. [1]. And math's biggest challenge, prove the Riemann hypothesis. [2]. Tackle the difficult Riemann hypothesis have been rejecting geniuses challenge for 150 years. [3]. The biggest challenge Prime mystery, history of mathematics, Riemann proved challenging. [4]. A new interpretation of the Riemann hypothesis. Zero point is all crosses the line. [5]. Elementary pulsation principle opens the doors of Lehman expected certification.
Category: Number Theory

[3] viXra:1602.0065 [pdf] submitted on 2016-02-05 14:44:44

Another Bold Conjecture on Fermat Pseudoprimes

Authors: Marius Coman
Comments: 2 Pages.

In my previous paper “Bold conjecture on Fermat pseudoprimes” I stated that there exist a method to place almost any Fermat pseudoprime to base two (Poulet number) in an infinite subsequence of such numbers, defined by a quadratic polynomial, as a further term or as a starting term of such a sequence. In this paper I conjecture that there is yet another way to place a Poulet number in such a sequence defined by a polynomial, this time not necessarily quadratic.
Category: Number Theory

[2] viXra:1602.0058 [pdf] submitted on 2016-02-05 08:43:58

Bold Conjecture on Fermat Pseudoprimes

Authors: Marius Coman
Comments: 2 Pages.

In many of my previous papers I showed various methods, formulas and polynomials designed to generate sequences, possible infinite, of Poulet numbers or Carmichael numbers. In this paper I state that there exist a method to place almost any Fermat pseudoprime to base two (Poulet number) in such a sequence, as a further term or as a starting term.
Category: Number Theory

[1] viXra:1602.0051 [pdf] submitted on 2016-02-04 15:34:08

A List of 15 Sequences of Poulet Numbers Based on the Multiples of the Number 6

Authors: Marius Coman
Comments: 3 Pages.

In previous papers, I presented few applications of the multiples of the number 30 in the study of Carmichael numbers, i.e. in finding possible infinite sequences of such numbers; in this paper I shall list 15 probably infinite sequences of Poulet numbers that I discovered based on the multiples of the number 6.
Category: Number Theory