Number Theory

1101 Submissions

[14] viXra:1101.0102 [pdf] submitted on 31 Jan 2011

Jiang And Wiles Proofs On Fermat Last Theorem(2)

Authors: Chun-Xuan Jiang
Comments: 18 pages.

D.Zagier (1984) and K.Inkeri(1990) said[7]: Jiang mathematics is true, but Jiang determinates the irrational numbers to be very difficult for prime exponent p>2. In 1991 Jiang studies the composite exponents n=15,21,33,...,3p and proves Fermat last theorem. In 1986 Gerhard Frey places Fermat last theorem at the elliptic curve that is Frey curve. Andrew Wiles studies Frey curve. In 1994 Wiles proves Fermat last theorem. Conclusion:Jiang proof is direct and simple,but Wiles proof is indirect and complex.
Category: Number Theory

[13] viXra:1101.0092 [pdf] replaced on 4 Mar 2011

On Prime Factors in Old and New Sequences of Integers

Authors: Marco Ripà
Comments: This paper is 17 pages long and the Italian version has already been published here: (http://www.rudimathematici.com/bookshelf/bookshelfdb.php).

The paper shows that the only possible prime terms of the "consecutive sequence" (1,12,123,1234...) represent of the total, and their structure is explicited. This outcome is then extended to every permutation of their figures. The previous result is applied to a consistent subset of elements belonging to the circular sequence (resulting from the consecutive one), identifying moreover the 31 first primes. Therefore, a criterion is illustrated (further extendible) that progressively reduces the numerousness of the "candidate prime numbers". Section 3.3 is devoted to the solution of a similar problem. The last section introduces a new sequence which, although much larger, has the same properties as the previous ones, and it also proposes a few open problems.
Category: Number Theory

[12] viXra:1101.0091 [pdf] submitted on 28 Jan 2011

Fermat Last Theorem And Riemann Hypothesis (6)

Authors: Chun-Xuan Jiang
Comments: 18 pages

1637 Fermat wrote: "It is impossible to separate a cube into two cubes, or a biquadrate into two biquadrates, or in general any power higher than the second into powers of like degree: I have discovered a truly marvelous proof, which this margin is too small to contain." (6)
Category: Number Theory

[11] viXra:1101.0090 [pdf] submitted on 28 Jan 2011

Fermat Last Theorem And Riemann Hypothesis (5)

Authors: Chun-Xuan Jiang
Comments: 18 pages

1637 Fermat wrote: "It is impossible to separate a cube into two cubes, or a biquadrate into two biquadrates, or in general any power higher than the second into powers of like degree: I have discovered a truly marvelous proof, which this margin is too small to contain." (5)
Category: Number Theory

[10] viXra:1101.0089 [pdf] submitted on 28 Jan 2011

Fermat Last Theorem And Riemann Hypothesis (4)

Authors: Chun-Xuan Jiang
Comments: 20 pages

1637 Fermat wrote: "It is impossible to separate a cube into two cubes, or a biquadrate into two biquadrates, or in general any power higher than the second into powers of like degree: I have discovered a truly marvelous proof, which this margin is too small to contain." (4)
Category: Number Theory

[9] viXra:1101.0087 [pdf] submitted on 26 Jan 2011

Generation of DNA Codes & the Hexagrams of I Ching from the Principle of Existence

Authors: Huping Hu, Maoxin Wu
Comments: 6 pages

In this short paper, the authors briefly discuss their preliminary thoughts on the coding of DNA and the hexagrams of I Ching based on the principle of existence. It is shown that one may mathematically generate the DNA codes from the principle of existence. It is further shown that one may also mathematically generate the hexagrams of Chinese I Ching from the principle of existence.
Category: Number Theory

[8] viXra:1101.0086 [pdf] submitted on 26 Jan 2011

Jiang and Wiles Proofs on Fermat Last Theorem(1)

Authors: Chun-Xuan Jiang
Comments: 21 pages

In 1637 Fermat wrote: "It is impossible to separate a cube into two cubes, or a biquadrate into two biquadrates, or in general any power higher than the second into powers of like degree: I have discovered a truly marvelous proof, which this margin is too small to contain."
Category: Number Theory

[7] viXra:1101.0071 [pdf] submitted on 22 Jan 2011

Remarks on the Function η(n)

Authors: Petru Minut
Comments: 4 pages

In 1980, F.SMARANDACHE introduced (see [5]) the function ...
Category: Number Theory

[6] viXra:1101.0070 [pdf] submitted on 22 Jan 2011

New Progress on Smarandache Problems Research

Authors: Guo Xiaoyan, Yuan Xia
Comments: 147 pages, in Chinese

New Progress on Smarandache Problems Research
Category: Number Theory

[5] viXra:1101.0051 [pdf] submitted on 16 Jan 2011

The K-Number Sieve and K-Inclusion-Exclusion Formula, Principle and Harvest

Authors: Tong Xin Ping
Comments: 3 pages

1-Number Sieve: It is the Eratosthenes'-Number Sieve and the da Silva-Sylvester formula. 2-Number Sieve: We can obtain result of Goldbach' conjecture and the number of solutions of Goldbach problem. 3-Number Sieve: We can obtain result p3 in N= p3+pi P1 and 3-Inclusion-exclusion formula.
Category: Number Theory

[4] viXra:1101.0047 [pdf] submitted on 14 Jan 2011

The New Prime Theorems (1041)-(1090)

Authors: Chun-Xuan Jiang
Comments: 117 pages

Using Jiang function we are able to prove almost all prime problems in prime distribution. This is the Book proof. No great mathematicians study prime problems and prove Riemann hypothesis in AIM, CLAYMI, IAS, THES, MPIM, MSRI. In this paper using Jiang function J2 (ω) we prove that the new prime theorems (1041)-(1090) contain infinitely many prime solutions and no prime solutions.
Category: Number Theory

[3] viXra:1101.0032 [pdf] submitted on 7 Jan 2011

The New Prime Theorems (991)-(1040)

Authors: Chun-Xuan Jiang
Comments: 122 pages

Using Jiang function we are able to prove almost all prime problems in prime distribution. This is the Book proof. No great mathematicians study prime problems and prove Riemann hypothesis in AIM, CLAYMI, IAS, THES, MPIM, MSRI. In this paper using Jiang function J2 (ω) we prove that the new prime theorems (991)-(1040) contain infinitely many prime solutions and no prime solutions...
Category: Number Theory

[2] viXra:1101.0028 [pdf] submitted on 6 Jan 2011

Counter to Zhou's Criticism of Jones' Proof of the Irrationality of π and π2

Authors: Tim Jones
Comments: 5 pages

A geometric proof of the irrationality of π is given. It uses an evaluation of the area given by the product of two symmetric functions, together with bounds on the integral. The symmetric functions embed the assumption of rational π; one function is dependent on n; as the evaluation of the integral exceeds the upper bound for large n for any given rational π, a contradiction is obtained. This proof has been criticized, but here some counters to the criticism are offered.
Category: Number Theory

[1] viXra:1101.0022 [pdf] submitted on 4 Jan 2011

The New Prime Theorems (941)-(990)

Authors: Chun-Xuan Jiang
Comments: 98 pages

Using Jiang function we are able to prove almost all prime problems in prime distribution. This is the Book proof. No great mathematicians study prime problems and prove Riemann hypothesis in AIM, CLAYMI, IAS, THES, MPIM, MSRI. In this paper using Jiang function J2 (ω) we prove that the new prime theorems (941)-(990) contain infinitely many prime solutions and no prime solutions.
Category: Number Theory