| viXra.org > Number Theory > 2006 |
 |
 |
| viXra.org > Number Theory > 2006 |
|
|
[25] viXra:2006.0275 [pdf] submitted on 2020-06-30 03:57:29
Authors: Jorma Jormakka
Comments: 14 Pages.
The paper proves a theorem when a prime is not a congruent number. The interest of the paper is in the proof method that maybe can be generalized to non-primes. Form primes the theorem does not add to the present knowledge.
Category: Number Theory
[24] viXra:2006.0274 [pdf] submitted on 2020-06-30 11:20:47
Authors: Abde-laziz Ben Ideiss
Comments: 3 Pages.
This paper discusses a function of infinite formulas in determining prime numbers directly and in order.
Category: Number Theory
[23] viXra:2006.0273 [pdf] submitted on 2020-06-30 11:02:44
Authors: Satyam Roy
Comments: 2 Pages. An article that demonstrates a relation between natural number and square root
Discussion about a special relationship between square root and a rational number. the result is only valid in the real domain R, for any natural number N.
Category: Number Theory
[22] viXra:2006.0259 [pdf] replaced on 2020-09-08 17:56:11
Authors: J N Cook with G Volk, D Allen
Comments: 10 Pages. Fixed minor typos, removed logic statements from body, added detail to the appendix
A function υ(s) is derived that shares all the non-trivial zeros of Riemann’s zeta function ζ(s), and a novel representation of ζ(s) is presented that relates the two. From this the zeros of ζ(s) may be grouped according to two types: υ(s)=0 and υ(s)≠0. A direct algebraic proof of the Riemann hypothesis is obtained by setting both functions to zero and solving for two general solutions for all the non-trivial zeros.
Category: Number Theory
[21] viXra:2006.0254 [pdf] replaced on 2023-07-10 02:17:13
Authors: Theophilus Agama
Comments: 6 Pages. Revised according to the referee report
In this paper we show that the natural density $mathcal{D}[(U_m)]$ of Ulam numbers $(U_m)$ satisfies $mathcal{D}[(U_m)]=0$. That is, we show that for $(U_m)subset [1,k]$ then begin{align}lim limits_{klongrightarrow infty}frac{left |(U_m)cap [1,k]ight |}{k}=0.onumberend{align}
Category: Number Theory
[20] viXra:2006.0251 [pdf] replaced on 2020-07-02 19:49:39
Authors: Xuan Zhong Ni
Comments: 5 Pages.
In this article, we use method of a modified sieve of Eratosthenes to prove the prime and the twin prime theory.
Category: Number Theory
[19] viXra:2006.0232 [pdf] submitted on 2020-06-25 11:55:19
Authors: Juan Moreno Borrallo
Comments: 4 Pages.
In this paper is studied briefly the relationship between prime numbers and double factorials.
Category: Number Theory
[18] viXra:2006.0228 [pdf] submitted on 2020-06-25 14:26:39
Authors: Isaac Mor
Comments: 8 Pages. this is not a reflection formula!
I am using the eta function spirals to find a formula for all the center points of any spiral on the complex plane
This is based on my previous ideas about the center points of the zeta function
(I am currently working on some really nice ideas that relate to this I will update this pdf when needed)
Category: Number Theory
[17] viXra:2006.0226 [pdf] replaced on 2020-08-17 01:27:34
Authors: A. A. Frempong
Comments: 19 Pages. Copyright © by A. A. Frempong
The Goldbach Conjecture states that every even integer greater than 4 can be expressed as the sum of two odd primes. In this paper, the proof of Goldbach conjecture is guided by the approach for finding Goldbach partitions. This approach leads directly to evidence that every even integer greater than 4 is the sum of two odd primes. The main principle for finding Goldbach partitions from a known partition is the application of the addition axiom to a Goldbach partition equation. It is shown that given an equation for a Goldbach partition, one can produce a Goldbach partition for any even integer greater than 4. Beginning with the partition equation, 6 = 3 + 3, and applying the addition of a 2 to both sides of this equation, and subsequent equations, one obtained Goldbach partitions for over 180 consecutive even integers. The repetitive process involved in the partition production was compared to the repetitive process in compound interest calculations. A consequent generalized procedure also produced Goldbach partitions for the non-consecutive even integers, 100; 1000; 372,131,740; and 400,000,001,1000. An equation derived for the Goldbach partition shows that every even integer greater than 4 can be written as the sum of two odd prime integers.
Category: Number Theory
[16] viXra:2006.0212 [pdf] submitted on 2020-06-23 20:23:46
Authors: Reuven Tint
Comments: 5 Pages.
In the present paper, new types of Pythagorean equations are derived (which are countless) based on the irrational ones that generate them, complex and integer numbers, those proven the fact of the rehabilitation of the system of solutions of the Pythagorean Euclidean equations based on the identities I received. It is believed, starting with Euclid (the third century BC) to the present, that these (2) and (2a) - and only these formulas given in [1], [2], [3] cover all integer solutions of the Pythagorean equation (1). It will be proved below that this is not so: the system of solutions given in [1], [2], [3] is not complete, which is a breakthrough in number theory.
Category: Number Theory
[15] viXra:2006.0193 [pdf] submitted on 2020-06-21 04:06:51
Authors: Claude H. R. Dequatre
Comments: 17 Pages. Comments are welcome
A previous paper submitted to viXra by the author on 2020-06-07 (1) and more specifically its paragraph 3-5 was related to the generation of primefree integer sequences using, as a seed, a prime numbers subset, a recursive algorithm and a specific formula described again in the next background section of this paper extending the initial work.
Indeed, whereas two prime numbers seeds containing respectively the first 10^3 and 2*10^4 prime numbers were used in the initial study, the seed size range has been enlarged from 10^2 to 10^7 prime number terms. This allowed to confirm previous results and reinforced the so called primefree conjecture referenced CD-3 established from them.
(1)This paper entitled "Structures and Properties of Integer Sequences generated from prime and nonprime number seeds"can be downloaded at:
http://viXra.org/abs/2005.0056 under the viXra subject category: number theory and citation number: 2006.0056.
Category: Number Theory
[14] viXra:2006.0184 [pdf] submitted on 2020-06-19 15:30:28
Authors: Ryan Zielinski
Comments: 28 Pages. This work is licensed under the CC BY 4.0, a Creative Commons Attribution License.
In this paper we will look at sums of odd powers of Fibonacci and Lucas numbers of even indices. Our motivation will be conjectures, now theorems, which go back to Melham. Using the simple approach of telescoping sums we will be able to give new proofs of those results. Along the way we will establish inverse relationships for such sums and discover new integer sequences.
Category: Number Theory
[13] viXra:2006.0171 [pdf] submitted on 2020-06-18 14:01:10
Authors: Michael I. I. Nwogugu
Comments: 4 Pages.
Liptai, Németh, et. al. (2020) conjectured (and supposedly proved) that in the diophantine equation (3a−1)(3b−1)=(5c−1)(5d−1) in positive integers a≤b, and c≤d, the only solution to the title equation is (a,b,c,d)=(1,2,1,1). This article proves that the Liptai, Németh, et. al. (2020) conjecture and results are wrong, and that there is more than one solution for the equation (3a−1)(3b−1)=(5c−1)(5d−1). This article introduces “Existence Conditions” and new theories of “Rational Equivalence”, and a new theorem pertaining to the equation gu=fv.
Category: Number Theory
[12] viXra:2006.0170 [pdf] submitted on 2020-06-18 14:02:51
Authors: Michael I. C. Nwogugu
Comments: 5 Pages.
In this article, several joint-properties of the equations a2+b2=c2, and ax+by=cz, are introduced.
Category: Number Theory
[11] viXra:2006.0169 [pdf] submitted on 2020-06-18 14:03:53
Authors: Michael I. C. Nwogugu
Comments: 8 Pages.
This article shows that the Qu (2018) conjectures, the Yang & Fu (2018) conjectures, the Jiang (2020) Conjecture-#1, the Tao (2016) Conjecture-#1, the Cipu & Mignotte (2007) Conjecture and the Cipu (2007) Conjecture [all of which pertain to the system of Simultaneous Pell equations x2−(a2−1)y2=1 and y2−pz2=1] are wrong.
Category: Number Theory
[10] viXra:2006.0164 [pdf] submitted on 2020-06-18 14:10:16
Authors: Michael I. C. Nwogugu
Comments: 6 Pages.
This article develops “existence” properties for the equations x2+y2+z2+v2=dXYZV; And x2+y2+z2+v2+u2=dXYZVU, and xi+yi+zi + vi =dXYZV (where i is a positive integer); and the results are applicable where all variables are Integers (ie. proofs within the context of Sub-Rings). Collectively and individually, these equations have wide applications in Computer Science, Physics, Applied Math and Finance/Economics.
Category: Number Theory
[9] viXra:2006.0156 [pdf] submitted on 2020-06-17 19:29:42
Authors: Richard Zhang
Comments: 1 Page.
It is commonly thought that Euler's number, denoted as `e' is approximately equal to
2.71828. In fact this error is found everywhere and even my CASIO fx-100AU PLUS calculator claims that e = 2.718281828... The following paper will explore this misconception
and analytically find another approximation for e.
Category: Number Theory
[8] viXra:2006.0123 [pdf] replaced on 2020-07-01 02:08:20
Authors: George Plousos
Comments: 6 Pages. corrected
Models are presented that describe the process of creating the Gray code and other similar codes without any calculation. These models are based on simple and rigid rules. Of the codes obtained in this way, only one does not correspond to a sequence ofOEIS, and it remains unknown whether it can be used somewhere.
Category: Number Theory
[7] viXra:2006.0074 [pdf] submitted on 2020-06-09 07:54:08
Authors: James Edwin Rock
Comments: 4 Pages.
Let Pn be the n_th prime. For twin primes Pn – Pn-1 = 2. Let X be the number of (6j –1, 6j+1) pairs in the closed interval [Pn, Pn^2]. The number of twin primes (TPAn) in [Pn, Pn^2] is
((Pn - an) /Pn)((Pn-1 - an-1) /Pn-1)((Pn-2 - an-2)/Pn-2)…((5 - a3) /5)(X). P3=5, 1.7 < an,..,a3 < 2.3. We exhibit a formula showing as Pn increases, the number of twin primes in the interval [Pn, Pn^2] also increases. Let Pn – Pn-1 = c. For n ≥ 4, (TPAn-1)(1+(2c –2)/2Pn-1+(c2–2c)/2Pn-1^2) < TPAn
Category: Number Theory
[6] viXra:2006.0056 [pdf] submitted on 2020-06-07 09:51:34
Authors: Claude H. R. Dequatre
Comments: 71 Pages. Comments are welcome
A specific recursive algorithm and three fomulas have been used to generate integer sequences from prime and nonprime numbers seeds.
After a few generations, some growing structures have been identified in these integer sequences, whereas such structures were absent when a subset of natural numbers was used as an alternative seed.
The sum of the reciprocals of primes of these integer sequences, well fitted by models of the form a*ln(ln(n)) + b, were calculated. Their distances to that of the harmonic series summed only over the primes were estimated and compared to the Meissel-Mertens constant.
Finally, the algorithm used with one of the three formulas led after a few iterations to the production of long primefree sequences containing large numbers and allowed to establish a so called primefree sequences conjecture.
Category: Number Theory
[5] viXra:2006.0054 [pdf] submitted on 2020-06-07 11:22:08
Authors: Jabari Zakiya
Comments: 32 Pages. More current/better versions of twin primes code in paper done in D, Nim, Rust and Crystal languages.
This paper describes the mathematical foundation of Prime Generators and their use in creating a fast Twin Primes Segmented Sieve of Zakiya (SSoZ), and also their applications to Number Theory, including Mersenne Primes, creating an exact Prime-counting Function, and implications for the Riemann Hypothesis.
Category: Number Theory
[4] viXra:2006.0053 [pdf] replaced on 2024-05-20 21:57:26
Authors: Jabari Zakiya
Comments: 23 Pages. New material and corrections.
The paper uses the structure and math of Prime Generators to show there are an infinity of twin primes, proving the Twin Prime Conjecture, as well as establishing the infinity of other k-tuples of primes.
Category: Number Theory
[3] viXra:2006.0046 [pdf] replaced on 2024-03-19 05:54:19
Authors: Theophilus Agama
Comments: 10 Pages. This paper has been technically and substantially improved.
Using the method of compression we improve on the current lower bound of Heilbronn's triangle problem. In particular, by letting $Delta(s)$ denotes the minimal area of the triangle induced by $s$ points in a unit disc. Then we have the lower boundbegin{align}Delta(s)gg frac{log s}{ssqrt{s}}.onumberend{align}
Category: Number Theory
[2] viXra:2006.0029 [pdf] submitted on 2020-06-03 15:14:49
Authors: Brian Scannell
Comments: 16 Pages.
We look at the pair correlation of the Riemann zeros at larger ranges. The evolution of this curve computed at different ranges is shown. The ripply shape of this curve is examined using spectral analysis. There seems to be a main spectral peak and possibly some other structures. The percentage RMS in the peak is shown. The results are compared to the spectrum of both noise and Montgomery’s pair correlation conjecture function . The pair correlation of unnormalised zeros shows dips at the zero positions.
Category: Number Theory
[1] viXra:2006.0005 [pdf] replaced on 2020-06-13 10:31:43
Authors: BOULAY Jean-Yves
Comments: 14 Pages. Continuation of the paper "The ultimate numbers and the 3/2 ratio"
According to new mathematical definitions, the set (ℕ) of whole numbers is subdivided into four subsets (classes of numbers), one of which is the fusion of the sequence of prime numbers and numbers zero and one. This subset, at the first level of complexity, is called the set of ultimate numbers. Three other subsets, of progressive level of complexity, are defined since the initial definition isolating the ultimate numbers and the non-ultimate numbers inside the set ℕ. The interactivity of these four classes of whole numbers generates singular arithmetic arrangements in their initial distribution, including exact 3/2 or 1/1 value ratios.
Category: Number Theory
| Third-Party Links: |
|