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| viXra.org > Number Theory > 2010 |
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[21] viXra:2010.0222 [pdf] replaced on 2020-10-31 10:56:35
Authors: Abdelmajid Ben Hadj Salem
Comments: Pages.
In this paper about the $abc$ conjecture, assuming the condition $c<rad^2(abc)$ holds, and the constant $K(\epsilon)$ is a smooth function, having a derivative for $\epsilon \in ]0,1[$, then we give the proof of the $abc$ conjecture.
Category: Number Theory
[20] viXra:2010.0199 [pdf] submitted on 2020-10-24 11:46:21
Authors: Kunle Adegoke
Comments: 10 Pages.
We derive new infinite series involving Fibonacci numbers and Riemann zeta numbers. The calculations are facilitated by evaluating linear combinations of polygamma functions of the same order at certain arguments.
Category: Number Theory
[19] viXra:2010.0189 [pdf] submitted on 2020-10-23 08:49:39
Authors: Marino Sumo
Comments: 9 Pages.
Let H̃ be a right-irreducible, contra-characteristic, pairwise commutative manifold. In [23, 36, 15],
the authors address the compactness of algebraic topoi under the additional assumption that − ζ̃(y) >
ρ 00 0, . . . , BA( Ḡ) . We show that Φ > −1. The work in [35, 21] did not consider the associative case. In [17], the authors address the smoothness of real, Turing, sub-continuously D-Gödel random variables under the additional assumption that O > kT k.
Category: Number Theory
[18] viXra:2010.0157 [pdf] submitted on 2020-10-20 19:45:33
Authors: Theophilus Agama
Comments: 6 Pages. [Corrections are made by viXra Admin]
In [paper] we study the master function and its connection to other arithmetic functions in number theory.
Category: Number Theory
[17] viXra:2010.0146 [pdf] submitted on 2020-10-19 10:21:53
Authors: Marino Sumo
Comments: 11 Pages.
Let τ be an almost elliptic morphism. Recent interest in finitely right-free monoids has centered on constructing pseudo-analytically maximal
groups. We show that every continuously negative system is degenerate, uncountable and invariant. In this setting, the ability to construct almost
surely closed, almost surely hyper-empty homeomorphisms is essential. It would be interesting to apply the techniques of [11] to natural functors.
Category: Number Theory
[16] viXra:2010.0142 [pdf] submitted on 2020-10-18 19:56:54
Authors: Olvine Dsouza
Comments: Pages. [Corrections made to conform with the requirements on the Submission Form]
This research is all about the biggest question... is it possible that without using factorization method can we find two prime numbers factors of any given product (composite number)? Answer is yes.... We have found the formula method that proves how additive property of prime numbers has direct relation with its multiplicative property and how it can help to find any two multiplied prime factors of given composite number.
Category: Number Theory
[15] viXra:2010.0120 [pdf] submitted on 2020-10-16 20:52:41
Authors: Theophilus Agama
Comments: 8 Pages.
In this paper we formulate and prove several variants of the Erdos-Turan additive bases conjecture.
Category: Number Theory
[14] viXra:2010.0114 [pdf] submitted on 2020-10-16 08:27:56
Authors: Victor Sorokine
Comments: 2 Pages. Великая теорема Ферма. Доказательство за 1 операцию умножения
After multiplying Fermat's equality by d^n, where prime n>2, d is a single-digit number with base n, 0<d<n, the penultimate digit in the number d^n is not zero (such exists!), the equality turns into inequality.
После умножения равенства Ферма на d^n, где простое n>2, d - однозначное число в счислении с базой n, 0<d<n, предпоследняя цифра в числе d^n не равна нулю (такая существует!), равенство превращается в неравенство.
Category: Number Theory
[13] viXra:2010.0113 [pdf] submitted on 2020-10-16 08:30:32
Authors: Victor Sorokine
Comments: Pages.
After multiplying Fermat's equality by d^n, where prime n>2, d is a single-digit number with base n, 0<d<n, the penultimate digit in the number d^n is not zero (such exists!), the equality turns into inequality.
Category: Number Theory
[12] viXra:2010.0108 [pdf] submitted on 2020-10-15 20:19:42
Authors: Dmitri Martila
Comments: 7 Pages. Rejected by many top journals without review
There are tens of self-proclaimed proofs for the Riemann Hypothesis and only 2 or 4 disproofs of it in arXiv. To this Status Quo I am adding my very short and clear results even without explicit mentioning prime numbers. One of my breakthroughs uses the peer-reviewed achievement of Dr.~Sol\'e and Dr.~Zhu, published just 4 years ago in a serious mathematical journal INTEGERS.
Category: Number Theory
[11] viXra:2010.0105 [pdf] submitted on 2020-10-15 20:21:45
Authors: Kunle Adegoke
Comments: 21 Pages.
We show how every power series gives rise to a Fibonacci series and a companion series involving Lucas numbers. For illustrative purposes, Fibonacci series arising from trigonometric functions, inverse trigonometric functions, the gamma function and the digamma function are derived. Infinite series involving Fibonacci and Bernoulli numbers and Fibonacci and Euler numbers are also obtained.
Category: Number Theory
[10] viXra:2010.0100 [pdf] submitted on 2020-10-15 11:16:47
Authors: J. F. Meyer
Comments: 8 Pages. Concerns Riemann Hypothesis
This investigation is a product of the ongoing scientific inquiry ' whence human suffering? ', the same encountering a critical need to call into serious question the long-standing π "approximation" methodolgy (ie. of exhaustion) employed by (and ever since) Archimedes (late, c. 287 – c. 212 BCE).
Category: Number Theory
[9] viXra:2010.0092 [pdf] submitted on 2020-10-13 20:14:14
Authors: Shekhar Suman
Comments: 6 Pages. [Corrections are made by viXra Admin]
Riemann's Xi function is defined as ξ(s) = [...]. ξ(s) is an entire function whose zeroes are the non trivial zeroes of ζ(s) All the non trivial zeros of the Riemann zeta function lie inside the critical strip 0 < R(s) < 1. In this paper[,], we use product representation of Riemann Xi function and
Schwarz Reflection principle to conclude that the Riemann Hypothesis is true.
Category: Number Theory
[8] viXra:2010.0089 [pdf] submitted on 2020-10-13 08:05:16
Authors: Antoine Balan
Comments: 3 Pages.
We make a new presentation of the Asymptotic Riemann Hypothesis which is not Riemann Hypothesis but a nearby simpler problem.
Category: Number Theory
[7] viXra:2010.0087 [pdf] submitted on 2020-10-13 08:41:11
Authors: Korn Rakpradit
Comments: 50 Pages.
In mathematics we require a proof for any hypothesis .But in the past 160 years ago a man called Bernhard Riemann refused to give a proof for his hypothesis about zeta function which he thought would be the formula for the number of primes less than a given number ‘x’. He might have a very ‘serious’ reason for not proving this. But for me, after five years of attempt to stalk his papers and using only a high school mathematical knowledge and/or a little bit higher,I can say that all high school student can learn how to prove this hypothesis whether it is right or wrong. Let me show you the proof.
Category: Number Theory
[6] viXra:2010.0077 [pdf] submitted on 2020-10-11 11:15:54
Authors: Juan Elias Millas Vera
Comments: 4 Pages. If you want to make me a comment you can write to me at juanmillaszgz@gmail.com
In this new nomenclature of operators, I show how it is possible to invent four new types of operators. I define some of their properties and I show a practical application solving theoretically the problem of how many primes there are less than a given number.
Category: Number Theory
[5] viXra:2010.0035 [pdf] replaced on 2020-12-31 04:59:56
Authors: Pranjal Jain
Comments: 7 Pages.
The aim of this paper is to generalize problem 3 of the 2019 PROMYS exam, which asks to show that the last 10 digits (in base 10) of t_n are same for all n >= 10, where t_0 = 3 and t_(k+1) = 3^(t_k). The generalization shows that given any positive odd integer p, t_m is congruent to t_n modulo [(p^2)+1]^n for all m >= n >= 1, where t_0 = p and t_(k+1) = p^(t_k)
Category: Number Theory
[4] viXra:2010.0031 [pdf] replaced on 2020-10-09 09:12:04
Authors: Jean-max Coranson-Beaudu
Comments: 3 Pages.
Riemann's hypothesis ([1],[2],[3],[6]) , formulated in 1859, concerns the location of the zeros of Riemann's Zeta function. The history of the Riemann Hypothesis is well known. In 1859, the German mathematician B. Riemann presented a paper to the Berlin Academy of Mathematic. In that paper, he proposed that this function, called Riemann-zeta function takes values 0 on the complex plane when s=0.5+it . This hypothesis has great significance for the world of mathematics and physics.([4]) This solutions would lead to innumerable completions of theorems that rely upon its truth. Over a billion zeros of the function have been calculated by computers and shown that all are on this line s = 0.5+it. In this paper we show that Riemann's function (xi) ��, involving the Riemann’s (zeta) �� function, is holomorphic and is expressed as an infinite polynom product in relation to their zeros and their conjugates.([5],[7]) By applying the functional equation of symmetry
��(1 − ��) = ��(��) , we deduce a relation between each zero of the function �� and its conjugate. We obtain the searched result: the real part of all zeros is equal to 1/2.
Category: Number Theory
[3] viXra:2010.0019 [pdf] replaced on 2020-10-08 19:46:01
Authors: Jorma Jormakka
Comments: 19 Pages. This is the submitted version of the paper.
The paper proves the Riemann Hypothesis. Zeros and the pole of the Riemann zeta function zeta(s)
correspond to simple poles of f(s), the derivative of the logarithm of zeta(s). In Re{s}>1 the function f(s) has an absolutely convergent sum expression with negatively exponential terms. When the Taylor series of f(s) is evaluated
at a point (l,0), l>>1, the absolute values of the coefficients of the Taylor series decrease in a negatively exponential manner when l increases. The function f(s) has simple poles in the area Re{s}<1. The pole gives the function r/(s-s_k), which can be evaluated into a Taylor series at (l,0). The coefficients of the Taylor series of the pole decrease as 1/l as a function of l. This implies that in the sum of all poles of f(s) poles must cancel other poles so that the negatively exponential behavior of the coefficients of the Taylor series dominates. The function of x=1/l arising from the pole -1/(s-1) at s=1 is -x/(1-x). The poles of f(s) at even negative integers give the function -xC. These two negative functions cannot cancel poles s_k that are on the x-axis and 0
Category: Number Theory
[2] viXra:2010.0008 [pdf] replaced on 2020-10-19 09:51:22
Authors: Abdelmajid Ben Hadj Salem
Comments: Pages.
In this paper, we consider the abc conjecture. We give some progress in the proof of the conjecture c<rad^2(abc) in the case c=a+1.
Category: Number Theory
[1] viXra:2010.0004 [pdf] replaced on 2021-06-08 19:36:31
Authors: Arthur W. Draut
Comments: 22 Pages.
The traditional definition of the twin prime conjecture is that there is an infinite number of
twin primes. The traditional definition of a twin prime is a pair of primes separated by one
even number, e.g., 29 and 31. We expand this definition and prove the infinitude of two types
of twin primes.
Our primary vehicle for proving the twin prime conjecture is a structure that we call Eratos-
thenes’ Patterns, which are created by Eratosthenes’ Sieve. First, we describe Eratosthenes’
Sieve, then we describe Eratosthenes’ Patterns, then we give the proof.
The essence of our proof is to show that the number of prime twins between pn and p2
n approaches
infinity as n approaches infinity.
Category: Number Theory
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