| viXra.org > Number Theory > 2310 |
 |
 |
| viXra.org > Number Theory > 2310 |
|
|
[13] viXra:2310.0145 [pdf] replaced on 2024-01-15 08:50:48
Authors: Timothy Jones
Comments: 5 Pages. Expanded content per comments received.
Using the sum of the derivatives of an integer polynomial with Euler's formula we prove that pi is irrational. We show how the technique can be used to show e and pi's transcendence.
Category: Number Theory
[12] viXra:2310.0117 [pdf] submitted on 2023-10-24 19:43:17
Authors: Masashi Furuta
Comments: 8 Pages.
This paper is positioned as a sequel edition of [1]. First, as in [1], define "division sequence", "complete division sequence", "star conversion", and "extended star conversion". Next, we use Well-Founded Induction and Peirce's law to prove the Collatz conjecture. This proof uses the theorem proving system Idris.
Category: Number Theory
[11] viXra:2310.0115 [pdf] submitted on 2023-10-24 19:40:31
Authors: Xiaohui Li
Comments: 4 Pages.
This paper utilizes the fact that the prime factor among all factors in the root number rad (c) can only be a power of 1. Then, analyze all combinations of c that satisfy rad (c)=c, calculate the value of the combination, and find the maximum and minimum values of the root number rad, as well as the maximum exponent between them. Using this maximum exponent then an equivalent inequality is constructed to prove the ABC conjecture.
Category: Number Theory
[10] viXra:2310.0113 [pdf] submitted on 2023-10-25 00:17:20
Authors: Juan Moreno Borrallo
Comments: 5 Pages.
In this short paper we prove that for n ≥ 2953652287 it exists some prime number between nand n + log(n), improving the best known proved bounds for the maximum interval between anynumber and the nearest prime number, as well as the maximum difference between two consecutiveprime numbers (prime gap). We note that this result proves some open conjectures on prime gapsand maximum intervals between any number and the nearest prime number.
Category: Number Theory
[9] viXra:2310.0111 [pdf] submitted on 2023-10-24 01:26:55
Authors: Tai-Choon Yoon, Yina Yoon
Comments: 5 Pages.
According to the Riemann rearrangement theorem, when a sequence converges, the sum can be changed by rearranging the order of the sequence. However, the result cannot be changed simply by rearranging the order of any sequences. In the case of the alternating harmonic series exemplified by Riemann, even if the result was the same by chance, the sum of the series was obtained by ignoring the sum oflim┬( n→∞)u2061∑_(k=n)^(2n-1) 1/(k+1)=lnu20612.
Category: Number Theory
[8] viXra:2310.0110 [pdf] replaced on 2023-10-30 21:07:58
Authors: Pierre Lamothe
Comments: 15 Pages. In French
The algebra of transition functions between elements of generalized Collatz sequences has revealed the true nature of cycles. The structure of the cyclic invariant enables us to demonstrate both:
a) The Syracuse conjecture cannot be substantiated as absolute veracity because no matter the length, a random cycle is theoretically possible.
b) The Syracuse conjecture can only hold true in practice with exceedingly probable status due to the exponential decay of a cycle’s probability as a function of length.
Category: Number Theory
[7] viXra:2310.0083 [pdf] replaced on 2023-10-25 10:02:01
Authors: Emmanuil Manousos
Comments: 3 Pages. Dear Editor, I am replacing the article due to errors in Example 2. Thank you for hosting my work on vixra.org. Best regards Emmanuil Manousos
In this article we present an algorithm for finding the factors Q of composite Fermat numbers. The algorithm finds the Q factors with less tests than required through the equation 2n×K+1.
Category: Number Theory
[6] viXra:2310.0046 [pdf] submitted on 2023-10-10 21:48:11
Authors: Budee U. Zaman
Comments: 9 Pages.
The enigma of dividing zero by zero 0 0 has perplexed scholars across philosophy, mathematics, and physics, remaining devoid of a clear-cut solution. This lingering conundrum leaves us in an unsatisfactory position,as there emerges a genuine necessity for such divisions, particularly in scenarios involving tensor components that are both set at zero. This article endeavors to grapple with this profound issue by leveraging the insights of Einstein’s theory of special relativity. Surprisingly, when we wholeheartedly embrace the ramifications of this theory, it becomes evidentthat zero divided by zero must equate to one 00 = 1. Essentially, we are confronted with a pivotal decision: either embrace the feasibility and definition of dividing zero by zero, in accordance with Einstein’s theory of special relativity, or reevaluate the integrity of this fundamental theory itself. This exploration delves into the profound consequences arisingfrom this critical choice.
Category: Number Theory
[5] viXra:2310.0041 [pdf] submitted on 2023-10-10 01:15:19
Authors: Hashem Sazegar
Comments: 5 Pages.
Oppermance’ conjecture states that there is a prime number between n^2 and n^2 + n for every positive integer n,first we show that , All integer numbers between x^2 and x^2 + ϵx can be written as x^2 + i > 4p that 1 ≤ i ≤ ϵx andp = (x − m − 2)2 + j in which j is a number in intervals 1 ≤ j ≤ ϵ(x − m − 2),and then we prove generalization of Oppermance’ conjecture i.e there is a prime number in interval n^2 and n^2 + ϵn such that 0 < ϵ ≤ 1.
Category: Number Theory
[4] viXra:2310.0020 [pdf] submitted on 2023-10-04 07:27:08
Authors: Rolando Zucchini
Comments: 13 Pages.
In the chapter 12° of his most significant book LIBER ABACI, Leonardo Pisano known as Fibonacci (Pisa 1170-1240 (?)) proposed a problem on the reproduction of rabbits [*]. So many scholars deduced that he arrives to his famous numerical sequence starting from this problem. In this article is explained a new hypothesis. The Fibonacci sequence was generated by the iteration of a theorem on the Golden Section, and it is presumably that was the great Italian mathematician to state and demonstrate it. The theorem allow us to proof a lot of properties of Fibonacci numbers. [*] A man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced by the initial couple in a year supposing every couple each month produces a new pair that can reproduce itself from the second month?
Category: Number Theory
[3] viXra:2310.0019 [pdf] submitted on 2023-10-04 08:06:50
Authors: Juan Moreno Borrallo
Comments: 2 Pages.
In this brief note there are showed original formulations for the reciprocal of the Riemann zeta function evaluated at 1, and Mertens function.
Category: Number Theory
[2] viXra:2310.0012 [pdf] submitted on 2023-10-03 23:46:39
Authors: Parker Emmerson
Comments: 6 Pages.
The Riemann Hypothesis can be reworded to indicate that the real part of one half always balanced at the infinity tensor by stating that the Riemann zeta function has no more than an infinity tensor's worth of zeros on the critical line.
Category: Number Theory
[1] viXra:2310.0002 [pdf] replaced on 2023-10-10 02:13:49
Authors: Oussama Basta
Comments: 2 Pages. A better version
The Riemann zeta function is one of the most important functions in mathematics, but it is also one of the most difficult to compute. In this paper, we present a new closed formula for the Riemann zeta function at prime numbers. Our formula is based on a new function.
Category: Number Theory
| Third-Party Links: |
|