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[13] viXra:2404.0115 [pdf] submitted on 2024-04-23 19:08:16
Authors: Ryujin Choi
Comments: 4 Pages. In Russian (Correction made by viXra Admin - Future non-compliant submission will not be accepted))
[This paper gives an attempted proof of [the] Collatz conjecture[.]
Category: Number Theory
[12] viXra:2404.0099 [pdf] submitted on 2024-04-20 23:03:43
Authors: Zhiyang Zhang
Comments: 3 Pages.
In the process of searching for counterexamples of the Riemann hypothesis using a computer, I accidentally discovered the possibility of counterexamples in a region. After delving into the derivation of mathematical formulas, I found that a perfect mathematical expression can be used to describe them. The position of the counterexample is right next to the area where s=1.
Category: Number Theory
[11] viXra:2404.0095 [pdf] submitted on 2024-04-18 22:28:22
Authors: Julian Beauchamp
Comments: 9 Pages. (Author name added to the article by viXra Admin as required; also, please cite and list scientific references - Please conform in the future!)
In this paper, we observe how some well-known integer sequences when divided by powers of 10 and summed to infinity have a unique discrete value, similar to a person's `DNA'.
Category: Number Theory
[10] viXra:2404.0088 [pdf] submitted on 2024-04-17 18:19:17
Authors: Adrian M. Stokes
Comments: 11 Pages.
The prime numbers ≥ 5 within a finite sequence of natural numbers can be found arithmetically by calculating all of the values of 6n-1 and 6n+1 that fall within the sequence and subtracting the composites given by (6n_1±1)(6n_2±1), where n is a natural number. For a given value of n_1, successive (6n_1-1)(6n_2+1), (6n_1-1)(6n_2-1) and (6n_1+1)(6n_2+1) composites occur at a regular interval, which increases by 36 from one value of n_1 to the next. When combined, these regular but different intervals create disorder in the sequences of 6n-1 and 6n+1 composites, which in turn creates the apparent randomness of the primes in the sequence of natural numbers. Furthermore, {(6n_1-1)(6n_2-1)} and {(6n_1+1)(6n_2+1)} numbers are subsets of 6n+1 composites whereas the only subset of the 6n-1 composites is {(6n_1-1)(6n_2+1)}. This creates a slight inequality in the proportions of composites and primes between the sets {6n-1} and {6n+1}, which otherwise have an equal number of members overall.
Category: Number Theory
[9] viXra:2404.0085 [pdf] submitted on 2024-04-16 21:26:21
Authors: Mostafa Senhaji
Comments: 15 Pages.
In the infinite universe of numbers, the Syracuse conjecture emerges as a captivating enigma, defying mathematical conventions and arousing the curiosity of the most daring minds.
Category: Number Theory
[8] viXra:2404.0084 [pdf] submitted on 2024-04-16 21:19:45
Authors: Giovanni Di Savino
Comments: 3 Pages. (Note by viXra Admin: Please cite and list scientific references)
Euclid and other mathematicians have emonstrated that prime numbers are infinite and, not being able to state how many prime numbers there are and how much time and space is needed to know their value, to satisfy the twin prime conjecture or Goldbach's conjecture , it will never be possible to elaborate all the possible combinations and values u200bu200bthat can be obtained by adding two or three of the infinite prime numbers but it is possible to know all the possible combinations and values u200bu200bthat can be obtained by adding two or three of the prime numbers, known, which are less than or equal to 2n+1.
Category: Number Theory
[7] viXra:2404.0054 [pdf] submitted on 2024-04-11 17:09:50
Authors: Mathis Antonetti
Comments: 5 Pages.
In this notice, we introduce the problem of minimal dividing odd subsets for the even numbers and we show that the density of such subsets of $n$ elements is asymptotically normal (that is at least decreasing as $frac{1}{n}$). We argue that understanding the problem of minimal dividing oddsubset might lead to new approaches to solving NP-hard problems.
Category: Number Theory
[6] viXra:2404.0041 [pdf] submitted on 2024-04-09 00:47:00
Authors: Mostafa Senhaji
Comments: 8 Pages. In French (Translation made by viXra Admin - Future non-compliant submission will not be accepted)
The Goldbach Conjecture is like a bewitching enigma, a melody whose first notes always elude our reach, challenging our most brilliant minds to unravel its mystery.
Category: Number Theory
[5] viXra:2404.0040 [pdf] replaced on 2025-09-26 23:01:07
Authors: Dawit Geinamo
Comments: 73 Pages.
The objective of this study is to present rigorous proofs for Collatz conjecture and introduce some interesting behavior of the Kaakuma sequence that is a vast generalized form of Collatz sequence. We analyze the behavior of Kaakuma sequence such as scaling up, scaling down, translation, function iteration and uniform growth of inverse tree. In addition to this we investigate relationship of increasing rate, number of iterations of cycles, gap in cycles, and densities of cycles of the Kaakuma sequence and evaluate consistency of tree size density after scaling.Our investigation culminates in the formulation of a set of conjectures encompassing lemmas and postulates, which we rigorously prove using a combination of analytical reasoning, numerical evidence, and exhaustive case analysis. These results provide compelling evidence for the veracity of the Collatz conjecture and contribute to our understanding of the underlying mathematical structure.
Category: Number Theory
[4] viXra:2404.0037 [pdf] submitted on 2024-04-07 17:40:57
Authors: Radomir Majkic
Comments: 6 Pages.
The Lonely Runner conjecture finds its mathematical description in winding the runner's linear paths into the complete cycle, c-cycle, on the unit track circle. All runners, to finish the competition, must complete the c-cyclesimultaneously. Any collection BT mR_{cn}ET of the BT cnET integer speeds runners and maximum speed BT v_{cn} =nET is a subset of the enveloping collection BT mR_{n}={ 1,2,3,cdots,n}ET of the BT n,;n>cn,ETrunners with the maximum speed BT n.ET[0.50mm]The time period BT 1_{ct}=1/nET of the fastest runner, f-runner BT n,ET defines the set of BT nET right half open time f-segments of the measure BT 1_{ct},ET which cover the c-cycle time domain of the measure BT 1.ETThe winding mapping of the linear paths BT X(t)ET associates with the c-cycle Graph BT G,ET the union of the BT nET individual graphs BT g=(t,X(t)),ET reduced to the domain of the c-cycle. The time domain segmentation partitions the Graph BT GET into BT nET Subgraphs BT G_{i},ET each one on the one of the BT nET f-segments. The final Subgraph bundle sinks into the point BT (1,1).ETAt the end of the first f-segment, all the runners arranged into f-constellation at the BT nET fixed, stationary points on the unit circle in the sequence of the increasing speeds. However, at the final f-segment, the runners, on the way to the starting point, are arranged at the decreasing speed order at the same stationary points.The speed order inversion inverts the slope order of the graphs on the final Subgraph bundle.Finally, the infimum graph BT g_{n-1}ET of the Subgraph bundle of the BT n-1ET runner's mutual separation graphs, the graph of thelargest slope connects the points BT (0,n-1)1_{cl}ET and BT (1,1)1_{cl}.ETConsequently, the Lonely Runner conjecture is true on the set BT mR_{n},ET and must be true on any of its subset BT mR_{cn},ET
Category: Number Theory
[3] viXra:2404.0032 [pdf] submitted on 2024-04-06 13:13:52
Authors: Rédoane Daoudi
Comments: 1 Page.
Here I present one formula about π.
Category: Number Theory
[2] viXra:2404.0016 [pdf] submitted on 2024-04-03 13:56:17
Authors: Mohamed Sghiar
Comments: 7 Pages.
Prime numbers [See 1-7] are used especially in information technology, such as public-key cryptography , and recall that the distribution of prime numbers is closely related to the non-trivial zeros of the zeta function therefore related to the Riemann hypothesis.Here I introduce the function $circledS$: $ (X,z) longmapsto prod_{pinmathcal{P}} frac1{1-X/p^{z}} $ which is a generalization of the function $zeta $ of Riemann that I will use to prove the Riemann hypothesis.
Category: Number Theory
[1] viXra:2404.0005 [pdf] submitted on 2024-04-02 00:52:49
Authors: Sigrid M. L. Obenland
Comments: 5 Pages.
Over the centuries, numerous mathematicians have tried to proof Fermat’s Last Theorem. In the year 1994, Fermat’s Last Theorem in the form of a^m + b^m = c^m with a, b and c being natural numbers and m being a natural number > 2 was shown to be correct In this publication I demonstrate that the difference in volume of two cubes having different side lengths cannot be a cube in itself with a side length having the value of a natural number.This also holds for cubes having higher dimensions than three, since the surfaces of these cubes all consist of three-dimensional cubes.
Category: Number Theory
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