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[17] viXra:2409.0171 [pdf] submitted on 2024-09-30 22:21:28
Authors: Khazri Bouzidi Fethi
Comments: 2 Pages.
we will establish a relationship between the classic Riemann Zeta function and Gauss's estimate for the prime numbers for the sequence of ����= ������where s is a real s> 1. We will use The Dusarat 1999 inequality to show that P(x) ≃ π(x) or P(x) Gauss estimation of prime numbers P(x) =�������� and π(x) the function that counts prime numbers.The key to this proof is the sequence of ����= ������where s is a real s> 1
Category: Number Theory
[16] viXra:2409.0163 [pdf] submitted on 2024-09-29 16:00:03
Authors: Pedro Baselga-Salinas
Comments: 5 Pages.
In this article, the author inquires into a new property for a set of numbers containing the Sheldon prime as the first term that allows to calculate summations just by solving a simple multiplication.
Category: Number Theory
[15] viXra:2409.0160 [pdf] submitted on 2024-09-29 00:08:34
Authors: Deepak Ponvel Chermakani
Comments: 2 Pages.
Our previous paper derived a result that an eventual non-zero lower bound ofminimum(absolute(sin(mπθ)), over positive integers m less than n), for large positive integers n, is (2 / (sqrt(5) n)). In this paper, we use this result to develop a heuristic to estimate the upper bound of the last non-periodic zero of any given homogenous linear recurrence with integer coefficients and integer starting points
Category: Number Theory
[14] viXra:2409.0157 [pdf] submitted on 2024-09-29 00:09:25
Authors: Predrag Terzic
Comments: 1 Page.
Conjectured formula for pi is introduced.
Category: Number Theory
[13] viXra:2409.0142 [pdf] replaced on 2025-10-02 01:16:22
Authors: Liao Teng
Comments: 25 Pages.
In order to strictly prove from the point of view of pure mathematics Goldbach's 1742 Goldbach conjecture and Hilbert's twinned prime conjecture in question 8 of his report to the International Congress of Mathematicians in 1900, and the French scholar Alfond de Polignac's 1849 Polignac conjecture, By using Euclid's principle of infinite primes, equivalent transformation principle, and the idea of normalization of set element operation, this paper proves that Goldbach's conjecture, twin primes conjecture and Polignac conjecture are completely correct. In order to strictly prove a conjecture about the solution of positive integers of indefinite equations proposed by French scholar Ferma around 1637 (usually called Ferma's last theorem) from the perspective of pure mathematics, this paper uses the general solution principle of functional equations and the idea of symmetric substitution, as well as the inverse method. It proves that Fermar's last theorem is completely correct.
Category: Number Theory
[12] viXra:2409.0126 [pdf] replaced on 2026-04-21 17:57:13
Authors: Ciro Cesarano
Comments: 17 Pages.
By a simple extension of rearrangement definition of a simply converging series, at non standard model of analysis, the author finds a new formula for ζ* (s) with s C*complex hyperreal numbers set with a *> 0 and with s ≠1 .However this new formula is very easily extendable at the whole complex plane with s ≠1 . Notable result is that with the definition of " non standard rearrangement " the commutative property of addition continues to hold even for simply convergent series (such as harmonic series with alternate signs). Moreover the author, by means of the new formula of ζ*(s) and the corresponding functional equation, gives a proof of the Riemann hypothesis.
Category: Number Theory
[11] viXra:2409.0121 [pdf] submitted on 2024-09-24 02:08:12
Authors: YongGwon Pak, KumSong Jang, MyongHyok Sin1, NamHo Kim
Comments: 8 Pages.
This paper proposes an efficient numerical solution of Bagley-Torvik equation which shows vibrating process of a rigid plate immersed in a Newtonian fluid. The proposed approaches are proved to get numerical solution with high accuracy for fractional order differential equation of a version of different Bagley-Torvik equation by simulation.
Category: Number Theory
[10] viXra:2409.0119 [pdf] submitted on 2024-09-24 02:11:53
Authors: Kim Yong Nam, Choe Song Byok, Ri Kyong Hyok, Choe Jong Hyok
Comments: 13 Pages.
If we account the constraints on the incremental acceleration as well as the incremental rate of the control input in the control system, the physical limit of the actuator can be considered and the stress of the system can be reduced.This paper deals with the design of the model predictive controller with the constraint on the incremental acceleration of the control input. The discrete time state space model of the plant is extended to the augmented model which has the incremental acceleration of the control input as the new input. The quadratic cost function, which is based on the control error and the incremental acceleration of the control input, is adopted. Constraints on the plant output, the control input, its incremental rate and acceleration are accounted. This constrained MPC problem can be solved by the quadratic programming procedure.To select the reasonable sampling period and prediction horizon, the lower bound of the settling time is derived for the proposed MPC system. Numerical examples illustrate the validity and effectiveness of the proposed method.
Category: Number Theory
[9] viXra:2409.0087 [pdf] submitted on 2024-09-17 00:02:57
Authors: Oliver Couto
Comments: 3 Pages. (Note by viXra Admin: An abstract is required; also please cite and list scientific references)
Multiple of a sixth power is a sum of two cubes.
Category: Number Theory
[8] viXra:2409.0057 [pdf] submitted on 2024-09-11 20:03:36
Authors: Filiberto Marra
Comments: 17 Pages.
This study on prime numbers presents a method that allows us to know divisible numbers without performing complex calculation system using examination of composition of numbers. Example 143=11x13, 493=17x29. I can know all prime numbers with this examination of composed number.
Category: Number Theory
[7] viXra:2409.0048 [pdf] submitted on 2024-09-09 17:37:18
Authors: Edgar Valdebenito
Comments: 4 Pages.
The Gaussian integral is defined as the integral of the function exp(-x^2) over the entire real line. Mathematically, it is expressed as:integral from -infinity to infinity(exp(-x^2))dx=sqrt(pi). In this note we give some formulas related to the Gaussian integral.
Category: Number Theory
[6] viXra:2409.0031 [pdf] submitted on 2024-09-06 03:39:51
Authors: Walter A. Kehowski
Comments: 61 Pages.
Given $n=p_1^{e_1}cdots p_k^{e_k}$, there is a canonical isomorphism $mathbb{Z}_ncongmathbb{Z}_{p_1^{e_1}} oplus cdots oplus mathbb{Z}_{p_k^{e_k}}$. The spectral basis of $mathbb{Z}_n$ is an explicit realization of this isomorphism within $mathbb{Z}_n$ itself. This paper is a study of those numbers whose spectral basis consists of primes and powers. For example, if $M_p$ is a Mersenne prime with exponent $p$, then $2M_p$ has spectral basis ${M_p,2^{p}}$, while $2^pM_p$ has spectral basis ${M_p^2,2^{p}}$. Isospectral and isotropic numbers are introduced and many other numbers with interesting spectral bases are presented.
Category: Number Theory
[5] viXra:2409.0022 [pdf] replaced on 2024-10-18 20:04:01
Authors: Wiroj Homsup, Nathawut Homsup
Comments: 6 Pages. (Note by viXra Admin: For the last time, both author's names - Not in call caps -should be filled on the Replacement Form)
The Collatz conjecture considers recursively sequences of positive integers where n is succeeded by n/2 , if n is even or (3n+1)/2 , if n is odd. The conjecture states that for all starting values n the Collatz sequence eventually reaches a trivial cycle 1, 2, 1, 2u2026u2026. If the Collatz conjecture is false, then either there is a nontrivial cycle, or one sequence goes to infinity. In this paper, we construct a directed graph based on the union of infinite number of basic Collatz directed graphs. Each basic Collatz directed graph relates to each positive integer. We show that the directed graph is connected and covers all positive integers. There is only a trivial cycle and no sequence goes to infinity.
Category: Number Theory
[4] viXra:2409.0021 [pdf] replaced on 2025-04-04 01:06:53
Authors: Predrag Terzic
Comments: 3 Pages.
Polynomial time primality test for numbers of the form 4*3^n - 1 is introduced .
Category: Number Theory
[3] viXra:2409.0019 [pdf] replaced on 2024-09-15 00:30:55
Authors: Yung Zhao
Comments: 2 Pages.
We construct a sequence of consecutive primes. From the perspective of statistics, we analyze and handle them by the combination of the fundamental property of primes with James Maynard's result. It reveals that there are infinitely many pairs of primes which differ by two.
Category: Number Theory
[2] viXra:2409.0003 [pdf] submitted on 2024-09-01 19:45:03
Authors: Ahcene Ait Saadi
Comments: 5 Pages. (Name added to Article by viXra Admin as required - Please conform)
Pseudo derivatives. This is a kind of derivation that I apply to polynomials with several variables of degree n. Such that the set of solutions of the system of pseudo derivatives of a polynomial P, belong to the set of solutions of the polynomial P. With this very powerful mathematical tool, I manage to solve: -an infinity of Diophantine equations - -The equations of higher degrees -systems of linear and nonlinear equations with several variablesFinally, this calculation allows me to question the notion of 0/0.
Category: Number Theory
[1] viXra:2409.0001 [pdf] submitted on 2024-09-01 22:27:37
Authors: Philippe Sainty
Comments: 21 Pages.
Proofs of the conjectures of Legendre, Andrica, Oppermann, Brocard and their generalizations using Lgk function sequences: x--> sqrt(pk/pk+1).sqrt(x).ln(x) , pk , kth prime number , x between pk and pk+1; we use reasoning by recurrence and absurdity; we obtain gaps framings between two consecutive primes, as well as the number of primes between N² and (N+1)². Generalizations with Lqk : x-->racineqième(pk/pk+1)*racineqième(x)*ln(x).
Category: Number Theory
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