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[12] viXra:2302.0148 [pdf] submitted on 2023-02-28 18:36:48
Authors: Leszek Mazurek
Comments: 17 Pages.
In this paper we show that thorough understanding of numbers is possible only if we present them as value in relation to the certain reference measure. Commonly, we use number 1 as a reference measure, however, it does not have to always be 1, it can be any other number. To fully understand the meaning of numbers, we have to maintain their natural form which is a quotient of a value to a reference measure. Only by keeping this form we can do mathematics properly and appreciate its natural beauty.
Category: Number Theory
[11] viXra:2302.0098 [pdf] replaced on 2023-02-25 07:05:48
Authors: Victor Sorokine
Comments: 2 Pages. Please replace text 2302.0098 with an amended version, because you did NOT publish the last version - "viXra new submission Result #14527104". OR post #14527104. Sincerely, Victor Sorokin
In equivalent equality, the number A^n+B^n-C^n ends with the digit 1.
Category: Number Theory
[10] viXra:2302.0093 [pdf] submitted on 2023-02-19 13:40:53
Authors: Edgar Valdebenito
Comments: 2 Pages.
Here we aim at presenting further interesting identities about certain finite or infinite series involving generalized harmonic numbers.
Category: Number Theory
[9] viXra:2302.0087 [pdf] submitted on 2023-02-19 02:58:09
Authors: Miguel Cerdá Bennassar
Comments: 11 Pages.
The purpose of this argument is to distribute a natural number (c) between (a) and (b), know the number of unique options (n) to do so, and calculate the values of (a) and (b). Obviously (c) is also the result of the sum of (a) and (b), but we have to see it as a consequence of the distribution, not as an end.Distribution of (C), an even natural number ≥2, between (A) and (B) in their (N) possible and unique options to do so.
Category: Number Theory
[8] viXra:2302.0076 [pdf] submitted on 2023-02-17 07:09:58
Authors: Miguel Cerdá Bennassar
Comments: 3 Pages.
In this paper, the properties of the digital root of numbers are analyzed and a possible connection with the sequences of the Collatz Conjecture is sought.
Category: Number Theory
[7] viXra:2302.0054 [pdf] submitted on 2023-02-12 01:57:11
Authors: Giovanni Di Savino
Comments: 6 Pages. (Corrections made by viXra Admin to conform with scholarly norm)
Euclid's algorithm can generate even perfect numbers, not only with prime numbers of "Mersenne" but it can generate even perfect numbers, with all prime numbers less than each of the infinite powers 2^n and will assume the form (2^ n - (1+2*n))*2^(n-1). Euclid's algorithm, but with the form: (prime ≥3^n -2) * prime ≥3^(n-1)), generates odd perfect numbers generated by primes distant 2 from the result of a power of a prime number ≥3^n, but with all prime numbers less than 2 or more distant than 2 , all odd perfect numbers are generated and the algorithm will have the following form: (prime ≥3^n -(2+2* n≥0)) * prime ≥3^(n-1)). In the same power, prime number ≥3^n, prime numbers less than prime ≥3^n are distinguished by their distance from the result of prime ≥3^n.
Category: Number Theory
[6] viXra:2302.0049 [pdf] replaced on 2023-10-20 16:07:26
Authors: Jim Rock
Comments: 10 Pages.
Collatz sequences are formed by dividing an even number by two until it is odd. Then multiply by three and add one to get an even number. The Collatz conjecture states that if this process is repeated you always get back to one. Using geometric series summations we prove that a connected Collatz Structure exists, which contains all positive integers exactly once. The terms of the Collatz Structure are joined together via the Collatz algorithm. Thus, every positive integer forms a Collatz sequence with unique terms terminating in the number one.
Category: Number Theory
[5] viXra:2302.0046 [pdf] submitted on 2023-02-11 02:28:51
Authors: Victor Sorokine
Comments: 2 Pages. (Note by viXra Admin: Please avoid repetition)
After transforming (using the Little Theorem) each of the numbers A, B, C to the form n^m - 1, the impossibility of Fermat's equality becomes obvious.
Category: Number Theory
[4] viXra:2302.0037 [pdf] submitted on 2023-02-10 01:25:45
Authors: Hongyuan Ye
Comments: 13 Pages.
This paper redefines the Collatz conjecture and proposes the equivalence Collatz conjecture, which is a necessary and sufficient condition for the Collatz conjecture. The Collatz transform is divided into Collatz even transform and Collatz odd transform. The scale coefficient of Collatz even transform is 0.5, and the scale coefficient of Collatz odd transform is greater than 1.5, but less than 1.501. Furthermore, In the process of Collatz transforms, the probability of Collatz even transforms and that of Collatz odd transforms are equal, and both of them are 0.5. Through the above analysis of the characteristics of Collatz transforms, it can be concluded: Take any positive integer N greater than 1, perform Collatz transforms on N for m times, when m is large enough, the Collatz transform result Nm must be less than its initial value N. That is, the equivalent Collatz conjecture is true, then the Collatz conjecture must also be true. Based on binomial distribution and normal distribution, it is deduced that any positive integer N greater than 1, the number of equivalent Collatz transforms mce = 100 * (1+ log N), then the number of Collatz transforms mc = (100 * (1+ log N)) * (N-1). Further analysis can be concluded that all the Collatz transform results must be unequal, so as to ensure that the transform results will not enter a dead loop during the Collatz transform process.
Category: Number Theory
[3] viXra:2302.0021 [pdf] replaced on 2023-02-07 14:04:25
Authors: R. Daoudi
Comments: 4 Pages.
A Mersenne number M_n is defined such as M_n = 2^n−1 and a Mersenne prime is theform of M_p = 2^p − 1 where p is a prime number.Lenstra, Pomerance and Wagstaff (called LPW conjecture) have conjectured that there areinfinite many Mersenne primes. According to them there are many infinite Mersenne primesof the form M_p = 2^p − 1 for some prime p.In this paper I try to reformulate the LPW conjecture using the Wilson’s theorem.
Category: Number Theory
[2] viXra:2302.0020 [pdf] submitted on 2023-02-06 16:31:26
Authors: Edgar Valdebenito
Comments: 5 Pages.
We give some integrals for ((4-sqrt(2))/8)*sqrt(pi)*zeta(3/2), where zeta(x) is the Riemann zeta function.
Category: Number Theory
[1] viXra:2302.0015 [pdf] replaced on 2023-11-21 23:50:51
Authors: Tsuneaki Takahashi
Comments: 7 Pages.
Investigation is tried about correctness of Collatz conjecture. There reverse procedure of Collatz conjecture procedure is used. Possibility of looping and divergence is eliminated.
Category: Number Theory
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