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[23] viXra:2204.0172 [pdf] replaced on 2023-08-30 22:02:36
Authors: Abdelmajid Ben Hadj Salem
Comments: 3 Pages. Submitted to Ramanujan Journal
In this paper, we consider the abc conjecture. Assuming that c<rad^2(abc) is true, we give anelementary proof that the abc conjecture is false using an equivalent statement.
Category: Number Theory
[22] viXra:2204.0166 [pdf] replaced on 2023-10-21 03:14:06
Authors: Wing K. Yu
Comments: 18 Pages.
In this paper along with the previous studies on analyzing the binomial coefficients, we will complete the proof of a theorem. The theorem states that for two positive integers n and k, if n ≥ (k −1), then there always exists at least a prime number p such that kn < p ≤ (k+1)n. The Bertrand-Chebyshev’s theorem is a special case of this theorem when k =1.
Category: Number Theory
[21] viXra:2204.0157 [pdf] submitted on 2022-04-27 21:22:50
Authors: Thomas Guyer
Comments: 8 Pages. (Corrections made by viXra Admin to conform with the requirements on the Submission Form)
we define �� , e , Lis(z) rational, proof the riemann hypothesis, and create a polynom and formula for ��.
Category: Number Theory
[20] viXra:2204.0151 [pdf] submitted on 2022-04-25 00:12:26
Authors: Tsuneaki Takahashi
Comments: 8 Pages.
This proves Collatz conjecture is correct using binary representation.
Each transition of generated numbers is determined in advance based on Collatz conjecture formula. But its path of transition is not so simple regarding to each initial value repeating increasing and decreasing.
Behavior of global flow to termination value 1 is investigated using concept of probability.
Category: Number Theory
[19] viXra:2204.0143 [pdf] submitted on 2022-04-24 21:28:09
Authors: Hao Li
Comments: 7 Pages.
This paper gives a detailed proof of Euler's theorem, which is the divergence of a series of reciprocals of the primes. The key idea of the proof is to assume the series converges and then complete the proof by contradiction.
Category: Number Theory
[18] viXra:2204.0139 [pdf] replaced on 2022-05-15 19:46:14
Authors: Marco Ripa
Comments: 7 Pages.
The starting point of our paper is Kashihara’s open problem #30, concerning the sequence A001292 of the OEIS, asking how many terms are perfect squares. We confirm his last conjecture up to the 100128-th term and provide a general theorem which rules out 4/9 of the candidates. Moreover, we formulate a new, provocative, conjecture involving the OEIS sequence A352991 (which includes all the terms of A001292, except the first one). Our risky conjecture states that all the perfect powers belonging to the sequence A352991 are perfect squares and they cannot be written as higher order perfect powers. This challenging conjecture has been checked for any integer smaller than 10111121314151617181920212223456789 and no counterexample has been found so far.
Category: Number Theory
[17] viXra:2204.0113 [pdf] submitted on 2022-04-19 21:20:36
Authors: Colin Power
Comments: 18 Pages. (Corrections made by viXra Admin to conform with the requirements on the Submission Form)
The first part of the solution to the Riemann Hypothesis that reveals why the trivial zeros will all appear at the canter of the n=0.5 Critical strip through the relational geometries found to form the golden and sliver ratio, that unify the infinite density of the zeta plain, thus producing only one solution whereby the analytic can be mapping into negative number space, by maintaining a 90 degree angle at all intersecting points across the number complex plain.
Category: Number Theory
[16] viXra:2204.0111 [pdf] submitted on 2022-04-19 17:14:42
Authors: Réjean Labrie
Comments: 2 Pages.
Let N, n and k be integers larger than 1. Then for all N there exists a minimum ceiling k such that for n>=N, if we cut the sequence of consecutive integers from 1 to n*(n+k) into n+k slices of length n, we always find at least a prime number in each of the first n+k slices at least.
It follows that π(n*(n+k)) > π(n*(n+k-1)) > π(n*(n+k-2)) > π(n*(n+k-3))> ...> π(2n)> π(n) where π(n) is the quantity of prime numbers smaller than or equal to n.
Category: Number Theory
[15] viXra:2204.0106 [pdf] replaced on 2022-09-02 00:54:35
Authors: Savinov Sergei
Comments: 2 Pages.
The preprint provides a calculation of the not allowed odd maxima of cyclic Collatz sequences.
Category: Number Theory
[14] viXra:2204.0105 [pdf] submitted on 2022-04-18 15:34:46
Authors: Lucian M Ionescu
Comments: 7 Pages. Article based on the ISU Algebra Seminar presentation available at https://about.illinoisstate.edu/lmiones/research/ with the same title.
Intuitively, prime numbers of ``Number systems'' (rings) are the building blocks of their elements.
We start from natural numbers and Gaussian integers to explain more general frameworks, like the structure theorem for finitely generated Abelian groups.
We end with a 1 million dollar puzzle, the Riemann Hypothesis, and point to the fact that prime numbers are dual to the Riemann zeros.
Some easy references are provided.
Category: Number Theory
[13] viXra:2204.0099 [pdf] submitted on 2022-04-17 19:58:48
Authors: Edoardo Gueglio
Comments: 10 Pages.
This paper identifies a correlation between a multiplicative property of number and the
additive property of all the sequences of consecutive number with equal sum.
Category: Number Theory
[12] viXra:2204.0086 [pdf] submitted on 2022-04-16 15:50:55
Authors: Arthur V. Shevenyonov
Comments: 3 Pages. effective PG algorithm/structure
A simple yet productive primes-generating relationship is proposed that amounts to a ‘qualitative recursion’ and arises from the [author’s] metaphor of a Prime Reservoir: p=p0*2^k*3^l-2^a*5^b. The study builds on one the size of 100 which can arbitrarily be re-scaled at various fill-in rates to accommodate prime sums (befitting the smaller primes) versus differences (pertaining to the larger ones yet to be reconsidered in terms of sums). The implied kernel X=p0 likewise proves to be prime, a^+b+k^+l=odd routinely promising primality.
Category: Number Theory
[11] viXra:2204.0080 [pdf] submitted on 2022-04-14 01:00:02
Authors: Grgo Čolak
Comments: 5 Pages.
When the sum of the prime factors of a composite number n results in another composite number m, we can take the sum of the prime factors of m. We can see if that is equal to yet another composite number s, and so on. Given any composite number n being greater than four, do we end up with every prime number via the method explained before? We present a constructive proof of this problem using number theory and logic. We find out that every prime number greater than three has finitely many prime friends (composite numbers whose prime factors added are the prime number itself). This is demonstrated through the use of the function 2k+3 and the partitions of prime numbers. In this way we also learn that we always end up with prime numbers through the sums of prime factors of composite numbers.
Category: Number Theory
[10] viXra:2204.0078 [pdf] submitted on 2022-04-14 23:07:43
Authors: Zakhar Pekhterev
Comments: 3 Pages. (Corrections made by viXra Admin to conform with scholarly norm)
Proof of the impossibility of the existence of a perfect cuboid.
Category: Number Theory
[9] viXra:2204.0054 [pdf] submitted on 2022-04-11 20:08:45
Authors: Takamasa Noguchi
Comments: 5 Pages.
Description of the algorithm for finding the q^k-th root of a. There is no basic difference in the calculation method created in the previous version. Some additions and changes have been made.
Category: Number Theory
[8] viXra:2204.0050 [pdf] submitted on 2022-04-11 10:26:37
Authors: Abdelmajid Ben Hadj Salem
Comments: Pages.
In this paper, assuming that the conjecture c<rad^2(abc) and Beal's Conjecture hold, I give, using elementary logic, the proof that the abc conjecture is false.
Category: Number Theory
[7] viXra:2204.0049 [pdf] submitted on 2022-04-11 11:18:09
Authors: Yuji Masuda
Comments: 3 Pages.
The main purpose of this chapter is to provide a more concise graphical explanation of the Barber pole system, the subject of my most recent paper.
Category: Number Theory
[6] viXra:2204.0033 [pdf] replaced on 2022-04-16 07:58:54
Authors: Timothy W. Jones
Comments: 7 Pages. Some readers gave corrections and suggested examples.
We show that using the denominators of the terms of $\zeta(n)-1=z_n$ as decimal bases gives all rational numbers in (0,1) as single decimals. We also show the partial sums of $z_n$ are not given by such single digits using the partial sum's terms. These two properties yield a proof that $z_n$ is irrational. As partials require denominators exceeding the denominators of their terms, possible single decimal convergence points are, using properties of decimal expansions, systematically eliminated.
Category: Number Theory
[5] viXra:2204.0031 [pdf] submitted on 2022-04-06 02:07:06
Authors: Yoshiki Ueoka
Comments: 4 Pages.
I propose a new approximate asymptotic formula for Prime number theorem.
The new formula is derived by the multi-point summation method. It has additional
term expressed with elementary function and gives better estimate of the
prime-counting function from small value to big value. It also satisfies asymptotic
formula with n -> ∞ limit.
Category: Number Theory
[4] viXra:2204.0029 [pdf] submitted on 2022-04-05 19:54:26
Authors: Yuji Masuda
Comments: 4 Pages.
The purpose of this short paper is to stop for a moment and explain my research clearly to you, as I feel that I have been updating my research with somewhat inadequate explanation.
Category: Number Theory
[3] viXra:2204.0028 [pdf] submitted on 2022-04-05 07:29:40
Authors: Savinov Sergey
Comments: 4 Pages.
In article the research of distribution of prime numbers is given in a natural row. The unknown
regularity in distribution density of prime numbers is described earlier and definition of an
algebraic form of this regularity is made.
Category: Number Theory
[2] viXra:2204.0017 [pdf] replaced on 2022-11-24 07:34:20
Authors: Yajun Liu
Comments: 4 Pages.
In this paper, we discuss the symmetry of N-domain and we find that using the symmetry characters of Natural Numbers we can give proofs of the Prime Conjectures: Twins Prime Conjecture、Goldbach Conjecture and Reimann Hypothesis.
Category: Number Theory
[1] viXra:2204.0010 [pdf] submitted on 2022-04-02 11:22:57
Authors: Yuji Masuda
Comments: 4 Pages.
In this report, the objective was to prove that the logarithm of a complex number is equal to its conjugate complex number and, in addition, to provide new insights into outer space.
Category: Number Theory
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