| viXra.org > Number Theory > 2012 |
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| viXra.org > Number Theory > 2012 |
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[16] viXra:2012.0225 [pdf] replaced on 2024-06-25 21:10:37
Authors: Shan Jian Wang
Comments: 7 Pages.
Conjecture: Any even number greater than 2 can be written as the sum of two prime numbers. Does the prime pair exist universally? If does, is the prime pair unique relatively? If not, how many prime pairs are there in an even? Method: Triangular lattice. Result: The number of prime pairs in an even can be expressed analytically and graphically.
Category: Number Theory
[15] viXra:2012.0219 [pdf] submitted on 2020-12-30 12:29:45
Authors: Timothy W. Jones
Comments: 12 Pages.
We prove that partial sums of Zeta(n)-1=zn are not given by any single decimal in a number base given by a denominator of their terms. These sets of single decimals we call decimal sets. This result, applied to all partials, shows that partials are excluded from an ever greater number of rational, possible convergence points, elements of these decimal sets. The limit of the partials is zn and the limit of the exclusions leaves only irrational numbers. Thus zn is proven to be irrational.
Category: Number Theory
[14] viXra:2012.0212 [pdf] submitted on 2020-12-29 08:46:59
Authors: Timothy W. Jones
Comments: 3 Pages.
Using for decimal bases the terms of e-2, we calculate partial sums and form open intervals for tails of partials. These intervals exclude all possible rational convergence points and thus show e-2 and hence e is irrational.
Category: Number Theory
[13] viXra:2012.0164 [pdf] replaced on 2023-08-11 23:14:14
Authors: Waldemar Puszkarz
Comments: 3 Pages. Originally published on Research Gate in March 2020
We conjecture that a formula that represents a difference between two primorials of different parities generates only odd abundant numbers for its arguments greater than 3. Using PARI/GP, we verified this conjecture for the arguments up to $4*10^4$. We also discuss another formula that generates only odd abundant numbers in an arithmetic progression and explain its origin in the context of the distribution of odd abundant numbers in general.
Category: Number Theory
[12] viXra:2012.0163 [pdf] replaced on 2023-08-11 11:19:49
Authors: Waldemar Puszkarz
Comments: 3 Pages. Originally published on Research Gate in March 2020.
We present a formula for the smallest possible numbers whose number of divisors is the $n$-th perfect number. The formula, that produces an integer sequence $a(n)$, involves the $n$-th Mersenne prime that appears both in an exponent of a power of 2 and in the product of consecutive odd primes (the odd primorial). While smallest in some sense, these numbers are among largest one can run into through an exercise in elementary number theory.
Category: Number Theory
[11] viXra:2012.0157 [pdf] submitted on 2020-12-21 18:09:00
Authors: Marc Schofield
Comments: 21 Pages. [Corrections made by viXra Admin to conform with the requirements on the Submission Form]
Finding cohesion in the seemingly abstract.
Category: Number Theory
[10] viXra:2012.0139 [pdf] submitted on 2020-12-19 13:07:56
Authors: Miguel Cerdá Bennassar
Comments: 4 Pages. [Corrections are made by viXra Admin to comply with the rules of viXra.org]
This paper studies other algorithms for the sequences in the Collatz Conjeture.
Category: Number Theory
[9] viXra:2012.0138 [pdf] submitted on 2020-12-18 15:30:15
Authors: Juan Elias Millas Vera
Comments: 2 Pages.
Henri Brocard posed two articles in 1876 and 1885 exposing the diophantine equation n!+1=m^2. It was also propose by Ramanujan. The unsolved problem says that it has not possible other solutions than n=4,5,7. In this paper I want to show a revision of the problem with the Stirling’s approximation to factorials.
Category: Number Theory
[8] viXra:2012.0120 [pdf] replaced on 2021-03-30 02:41:03
Authors: A. A. Frempong
Comments: 6 Pages. Copyright © by A. A. Frempong
By applying basic mathematical principles, the author surely, and instructionally, proves, directly, the original Beal conjecture which states that if A^x + B^y = C^z, where A, B, C, x, y, z are positive integers and x, y, z > 2, then A, B and C have a common prime factor. One will let r, s, and t be prime factors of A, B and C, respectively, such that A = Dr, B = Es, C = Ft, where D, E, and F are positive integers. Then, the equation A^x + B^y = C^z becomes D^xr^x + E^ys^y = F^zt^z. The proof would be complete after showing that the equalities, r^x = t^x, s^y = t^y and r = s = t, are true. The proof of the above equalities would involve showing that the ratios, (r^x)/(t^x) = 1 and (s^y)/(t^y) =1, which would imply that r = s = t. The main principle for obtaining relationships between the prime factors on the left side of the equation and the prime factor on the right side of the equation is that the power of each prime factor on the left side of the equation equals the same power of the prime factor on the right side of the equation. High school students can learn and prove this conjecture for a bonus question on a final class exam.
Category: Number Theory
[7] viXra:2012.0119 [pdf] submitted on 2020-12-15 10:31:56
Authors: Philippe E. Ruiz
Comments: 17 Pages.
The pattern of the primes is one of the most fundamental mysteries of mathematics. This paper introduces a core polynomial model for primes based on nested residual regressions. Residual nestedness reveals increasing polynomial intertwining and shows scale invariance, or at least strong self-similarity up to at least p = 15,485,863. Accuracy of prediction decreases as the prediction range increases, conversely, the increase in the number of models helps refine predictions holistically.
Category: Number Theory
[6] viXra:2012.0106 [pdf] submitted on 2020-12-14 19:57:19
Authors: Abdelmajid Ben Hadj Salem
Comments: 10 Pages. Submitted to the journal The Fibonacci Quartely. Comments welcome
In this paper, we consider the abc conjecture. In the first part, we give the proof of the conjecture c < rad ^{1.63}(abc) that constitutes the key to resolve the abc conjecture. The proof of the abc conjecture is given in the second part of the paper, supposing that the abc conjecture is false, we arrive in a contradiction.
Category: Number Theory
[5] viXra:2012.0086 [pdf] replaced on 2021-07-23 21:21:05
Authors: Dmitri Martila
Comments: 5 Pages. Submitted to the journal.
In this short note, I prove the abc conjecture.
You are free not to get enlightened about that fact. But please pay respect to new dispositions of the abc conjecture and research methods in this note.
Category: Number Theory
[4] viXra:2012.0085 [pdf] submitted on 2020-12-10 22:21:17
Authors: James Camacho
Comments: 2 Pages.
In this paper we use induction to prove that all roots of 2 are irrational.
Category: Number Theory
[3] viXra:2012.0041 [pdf] replaced on 2020-12-10 21:06:36
Authors: A. A. Frempong
Comments: 11 Pages. Copyright © by A. A. Frempong
Using the "scientific approach", the author proves directly the original Beal conjecture (and not the equivalent conjecture) that if A^x + B^y = C^z, where A, B, C, x, y, z are positive integers and x, y, z > 2, then A, B and C have a common prime factor. One will let r, s, and t be prime factors of A, B and C, respectively, where D, E, and F are positive integers, such that A = Dr, B = Es, C = Ft. Then, the equation A^x + B^y = C^z becomes D^xr^x + E^ys^y = F^zt^z. Seven numerical Beal equations were factored. Based on the consistent pattern of the structure of the relationships between the prime factors on the left sides of the equations and the prime factors on the right sides of the equations in the factorizations, the author conjectured the equalities, r^x = t^x and s^y = t^y, which would imply that r = s = t, and establish that the Beal conjecture is true. The proof would be complete after showing that r^x = t^x, s^y = t^y and r = s = t, The proof in this paper is an expansion of a previous paper (viXra:2001.0694. by the author. The proof of the above equalities will be complete after showing that the ratios, (r^x)/(t^x) = 1 and (s^y)/(t^y) =1. To accomplish these relationships, one will factor out r^x on the left side of the equation, D^xr^x + E^ys^y = F^zt^z, followed by factoring out s^y of the same equation. The main principle for obtaining relationships between the prime factors on the left side of the equation and the prime factor on the right side of the equation is that the greatest common power of each prime factor on the left side of the equation equals the same power of the prime factor on the right side of the equation. High school students can learn and prove this conjecture as a bonus question on a final class exam.
Category: Number Theory
[2] viXra:2012.0039 [pdf] replaced on 2021-07-30 20:46:32
Authors: Toshihiko Ishiwata
Comments: 12 Pages.
This paper is a trial to prove Riemann hypothesis according to the following process. 1. We create the infinite number of infinite series from one equation that gives ζ(s) analytic continuation to Re(s) > 0 and 2 formulas (1/2 + a + bi, 1/2 − a − bi) which show zero point of ζ(s). 2. We find that a cannot have any value but zero from the above infinite number of infinite series. Therefore zero point of ζ(s) must be 1/2 ± bi.
Category: Number Theory
[1] viXra:2012.0013 [pdf] replaced on 2021-01-07 06:38:04
Authors: Dante Servi
Comments: 8 Pages. Copyright by Dante Servi. With the revision [v3] I have again changed the description of the procedure, in order to make it more understandable.
With this article I illustrate my procedure (theoretically unlimited), able to reconstruct the distribution of prime numbers. The procedure is based on simple arithmetic calculations guided by a scheme that I cannot define other than graphical. The Eratosthenes sieve was the best of the first methods for finding prime numbers, but it has a limit; this procedure exceeds the limit. If there is a connection between my procedure and the Riemann hypothesis, it will be the mathematicians who will discover it.
Category: Number Theory
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