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[9] viXra:2102.0163 [pdf] replaced on 2021-07-16 10:53:32
Authors: Suaib Lateef
Comments: 8 pages
In this paper, we present two identities involving Fibonacci numbers and Lucas numbers. The first identity generalizes Vajda's identity, which in turn generalizes Catalan's identity, while the second identity is a corresponding result involving Lucas numbers. Binet's formulas for generating the nth term of Fibonacci numbers and Lucas numbers will be used in proving the identities.
Category: Number Theory
[8] viXra:2102.0161 [pdf] replaced on 2021-03-21 08:06:00
Authors: Theophilus Agama, Berndt Gensel
Comments: 7 Pages. The first proof of the Lemma is wrong and still under construction. So the current proof is conditional and will be completed.
In this paper we use a new method to study problems in additive number theory. We leverage this method to prove the Lemoine conjecture, a closely related problem to the binary Goldbach conjecture. In particular, we show by using the notion of circles of partition that for all odd numbers $n\geq 9$ holds
\begin{align*}
n=p+2q\mbox{ for not necessarily different primes }p,q.
\end{align*}
Category: Number Theory
[7] viXra:2102.0083 [pdf] replaced on 2021-04-11 12:39:26
Authors: J. Walter
Comments: 1 Page.
This short paper is about nontrivial zeros of Riemann's zeta function.
Category: Number Theory
[6] viXra:2102.0062 [pdf] submitted on 2021-02-11 20:40:56
Authors: Edgar Valdebenito
Comments: 2 Pages.
We give some remarks on Malmsten's integral.
Category: Number Theory
[5] viXra:2102.0056 [pdf] submitted on 2021-02-10 20:32:24
Authors: Oliver Couto
Comments: 5 Pages.
On the internet & math literature there is not much mention about the quintic equation, p(a^5+b^5 )=q(c^5+d^5 ). Since parameterization of fifth degree equations is generally hard the author has attempted to find numerical solutions to the above quintic equation by algebraic method. In the concluding note the author has mentioned an open problem regarding the above quintic equation.
Category: Number Theory
[4] viXra:2102.0044 [pdf] replaced on 2022-03-02 18:48:35
Authors: Jeet Kumar Gaur
Comments: 19 Pages.
This paper presents a new approach towards the Riemann Hypothesis. On iterative expansion of integration term in functional equation of the
Riemann zeta function we get sum of two series function. At the ‘nontrivial’ zeros of zeta function, value of the series is zero. Thus, Riemann hypothesis is false if that happens for an ‘s’ off the line <(s) = 1/2 ( the critical line). This series has two components f(s) and f(1 − s). For the hypothesis to be false one component is additive inverse of the other. From geometric analysis of spiral geometry representing the component series functions f(s) and f(1 − s) on complex plane we find by contradiction
that they cannot be each other’s additive inverse for any s, off the critical line. Thus, proving truth of the hypothesis.
Category: Number Theory
[3] viXra:2102.0034 [pdf] submitted on 2021-02-06 09:41:49
Authors: Mueiz Gafer KamalEldeen
Comments: 1 Page.
The concept of prime number as it is defined cannot be formulated in a general algebraic form and therefore cannot be used in a mathematical process of deductive reasoning
Category: Number Theory
[2] viXra:2102.0011 [pdf] submitted on 2021-02-02 11:45:02
Authors: Méhdi Pascal
Comments: 22 Pages.
This paper contains everything you need to know about the Agoh-Giuga conjecture, all the theorems related to this problem are given with the demonstrations well detailed so that they are easily readable to students, including the equivalence between the Agoh conjecture and Giuga conjecture, Theorem (36) is a new characterizes Carmichael numbers, it allows a combinatorial aspect of these numbers, at the end of this paper I give my remarks which show that it is possible to prove this conjecture if we focus on Carmichael's numbers, and not on Giuga's numbers.
Category: Number Theory
[1] viXra:2102.0005 [pdf] submitted on 2021-02-01 19:18:54
Authors: Jean-Max Coranson-Beaudu
Comments: 3 Pages.
The approach of this proof, is to show that whatever of the even number, it is always be decomposed into the difference of two odd numbers. Then, with the fundamental theorem of arithmetic, it can be show the necessary existence of a prime number Pi less than 2n when 2n is more than 3. We deduce that 2n is the difference of a prime number and an odd number. An arithmetic sequence of parameter n and first term Pi will be constructed to deduce that there is at least one prime number in the terms of this sequence by Dirichlet-Lejeune’s Theorem. We will show that whatever of 2n>3, there are two prime numbers �� �� and −2 �� + �� �� whose difference is equal to 2n.
Category: Number Theory
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