Number Theory

1103 Submissions

[13] viXra:1103.0094 [pdf] submitted on 23 Mar 2011

Brocard`s Problem. Variants of Brocard`s Problem

Authors: Martiros Khurshudyan
Comments: 2 pages.

In this article we considered an open problem. One of the problems in the list of open problems of General Number Theory, existing in [1], [2] is the Brocard`s Problem, asking to find integer values of n, for which n! + 1 = m2. 'Introduction' section is dedicated to the statement of the main problem. We presented some historical overview and known facts about this problem in the 'Historical overview and known facts' section , based on information presented in the web [1], [2]. In the section 'Variants of the Problem' several variants of the Problem are presented by author based on more general n! + A = k2 [4] equation and asked to find solutions for them.
Category: Number Theory

[12] viXra:1103.0092 [pdf] replaced on 8 Apr 2011

Generalized Fermat's Last Theorem (2) Rn = y14y24

Authors: Chun-Xuan Jiang
Comments: 6 pages.

In this paper we prove Rn = y1 4y24 has no nonzero integer solutions for n ≥ 2.
Category: Number Theory

[11] viXra:1103.0091 [pdf] submitted on 23 Mar 2011

Fermat's Last Theorem (1)

Authors: Chun-Xuan Jiang
Comments: 6 pages.

On the afternoon of July 19, 1978 this proof was disproved by Chinese mathematics institute of Academia Sinica. How tragic! We rewrite this paper.
Category: Number Theory

[10] viXra:1103.0081 [pdf] replaced on 2014-11-18 10:15:58

Collatz Problem and Conjecture. a Generalization of the Problem

Authors: Martiros Khurshudyan
Comments: 1 Page. reorganised version

The aim of this article is presents an open problem of Mathematics. We will talk and present shortly Collatz problem and conjecture to make clear our motivation for new problem. Introduction to the original Collatz problem is given as in [1],[2],[3],[4]. From our point of view a very properly introduction to the main problem. A genaralization is proposed as well as three questions are asked to a reader at the end of article, after definition of our problem. We thought, it is possible to develop a mathematical game based on Collatz problem. We leave this idea for future works.
Category: Number Theory

[9] viXra:1103.0070 [pdf] replaced on 4 Dec 2011

Patterns Related to the Smarandache Circular Sequence Primality Problem

Authors: Marco Ripà
Comments: 21 Pages.

In this paper, we show the internal relations among the elements of the circular sequence (1,12,21,123,231,312,1234,2341,...). We illustrate one method to minimize the number of the "candidate prime numbers" up to a given term of the sequence. So, having chosen a particular prime divisor, it is possible to analyze only a fixed number of the smallest terms belonging to a given range, thus providing the distribution of that prime factor in a larger set of elements. Finally, we combine these results with another one, also expanding the study to a few new integer sequences related to the circular one.
Category: Number Theory

[8] viXra:1103.0038 [pdf] submitted on 12 Mar 2011

Generalized Fermat's Last Theorem Rn = ...

Authors: Chun-Xuan Jiang
Comments: 4 pages

IIn this paper we prove (...) has infinitely many nonzero integer solutions. We prove (...) has no nonzero integer solutions.
Category: Number Theory

[7] viXra:1103.0016 [pdf] submitted on 5 Mar 2011

Fermat Last Theorem Controversy (6)

Authors: Chun-Xuan Jiang
Comments: 22 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 for prime exponent p>3[1].In 1986 Gerhard Frey places Fermat last theorem at elliptic curve ,now called a Frey curve.Andrew Wiles studies Frey curve.In 1994 Wiles proves Fermat last theorem[9,10].Conclusion:Jiang proof is direct and very simple,but Wiles proof is indirect and very complex. If China mathematicians and Academia Sinica had supported and recognized Jiang proof on Fermat last theorem,Wiles would not have proved Fermat last theorem,because in 1991 Jiang had proved Fermat last theorem[1].Wiles has received many prizes and awards, he should thank China mathematicians and Academia Sinica.To support and to publish Jiang Fermat last theorem paper is prohibited in Academia Sinica. Remark. Chun-Xuan Jiang,A general proof of Fermat last theorem(Chinese),Mimeograph papers,July 1978. In this paper using circulant matrix,circulant determinant and permutation group theory Jiang had proved Fermat last theorem for odd prime exponent. (6 again)
Category: Number Theory

[6] viXra:1103.0014 [pdf] submitted on 3 Mar 2011

Jiang and Wiles Who Has First Proved Fermat Last Theorem (3)

Authors: Chun-Xuan Jiang
Comments: 14 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 for prime exponent p>3[1].In 1986 Gerhard Frey places Fermat last theorem at elliptic curve ,now called a Frey curve.Andrew Wiles studies Frey curve.In 1994 Wiles proves Fermat last theorem[9,10].Conclusion:Jiang proof is direct and very simple,but Wiles proof is indirect and very complex. If China mathematicians and Academia Sinica had supported and recognized Jiang proof on Fermat last theorem,Wiles would not have proved Fermat last theorem,because in 1991 Jiang had proved Fermat last theorem[1].Wiles has received many prizes and awards, he should thank China mathematicians and Academia Sinica.To support and to publish Jiang Fermat last theorem paper is prohibited in Academia Sinica. Remark. Chun-Xuan Jiang,A general proof of Fermat last theorem(Chinese),Mimeograph papers,July 1978. In this paper using circulant matrix,circulant determinant and permutation group theory Jiang had proved Fermat last theorem for odd prime exponent. (3)
Category: Number Theory

[5] viXra:1103.0010 [pdf] submitted on 3 Mar 2011

Jiang and Wiles Who Has First Proved Fermat Last Theorem (6)

Authors: Chun-Xuan Jiang
Comments: 14 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 for prime exponent p>3[1].In 1986 Gerhard Frey places Fermat last theorem at elliptic curve ,now called a Frey curve.Andrew Wiles studies Frey curve.In 1994 Wiles proves Fermat last theorem[9,10].Conclusion:Jiang proof is direct and very simple,but Wiles proof is indirect and very complex. If China mathematicians and Academia Sinica had supported and recognized Jiang proof on Fermat last theorem,Wiles would not have proved Fermat last theorem,because in 1991 Jiang had proved Fermat last theorem[1].Wiles has received many prizes and awards, he should thank China mathematicians and Academia Sinica.To support and to publish Jiang Fermat last theorem paper is prohibited in Academia Sinica. Remark. Chun-Xuan Jiang,A general proof of Fermat last theorem(Chinese),Mimeograph papers,July 1978. In this paper using circulant matrix,circulant determinant and permutation group theory Jiang had proved Fermat last theorem for odd prime exponent. (6)
Category: Number Theory

[4] viXra:1103.0009 [pdf] submitted on 3 Mar 2011

Jiang and Wiles Who Has First Proved Fermat Last Theorem (5)

Authors: Chun-Xuan Jiang
Comments: 14 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 for prime exponent p>3[1].In 1986 Gerhard Frey places Fermat last theorem at elliptic curve ,now called a Frey curve.Andrew Wiles studies Frey curve.In 1994 Wiles proves Fermat last theorem[9,10].Conclusion:Jiang proof is direct and very simple,but Wiles proof is indirect and very complex. If China mathematicians and Academia Sinica had supported and recognized Jiang proof on Fermat last theorem,Wiles would not have proved Fermat last theorem,because in 1991 Jiang had proved Fermat last theorem[1].Wiles has received many prizes and awards, he should thank China mathematicians and Academia Sinica.To support and to publish Jiang Fermat last theorem paper is prohibited in Academia Sinica. Remark. Chun-Xuan Jiang,A general proof of Fermat last theorem(Chinese),Mimeograph papers,July 1978. In this paper using circulant matrix,circulant determinant and permutation group theory Jiang had proved Fermat last theorem for odd prime exponent. (5)
Category: Number Theory

[3] viXra:1103.0008 [pdf] submitted on 3 Mar 2011

Jiang and Wiles Who Has First Proved Fermat Last Theorem (4)

Authors: Chun-Xuan Jiang
Comments: 16 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 for prime exponent p>3[1].In 1986 Gerhard Frey places Fermat last theorem at elliptic curve ,now called a Frey curve.Andrew Wiles studies Frey curve.In 1994 Wiles proves Fermat last theorem[9,10].Conclusion:Jiang proof is direct and very simple,but Wiles proof is indirect and very complex. If China mathematicians and Academia Sinica had supported and recognized Jiang proof on Fermat last theorem,Wiles would not have proved Fermat last theorem,because in 1991 Jiang had proved Fermat last theorem[1].Wiles has received many prizes and awards, he should thank China mathematicians and Academia Sinica.To support and to publish Jiang Fermat last theorem paper is prohibited in Academia Sinica. Remark. Chun-Xuan Jiang,A general proof of Fermat last theorem(Chinese),Mimeograph papers,July 1978. In this paper using circulant matrix,circulant determinant and permutation group theory Jiang had proved Fermat last theorem for odd prime exponent. (4)
Category: Number Theory

[2] viXra:1103.0004 [pdf] submitted on 2 Mar 2011

Jiang and Wiles Who Has First Proved Fermat Last Theorem (2)

Authors: Chun-Xuan Jiang
Comments: 35 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 for prime exponent p>3[1].In 1986 Gerhard Frey places Fermat last theorem at elliptic curve ,now called a Frey curve.Andrew Wiles studies Frey curve.In 1994 Wiles proves Fermat last theorem[9,10].Conclusion:Jiang proof is direct and very simple,but Wiles proof is indirect and very complex. If China mathematicians and Academia Sinica had supported and recognized Jiang proof on Fermat last theorem,Wiles would not have proved Fermat last theorem,because in 1991 Jiang had proved Fermat last theorem[1].Wiles has received many prizes and awards, he should thank China mathematicians and Academia Sinica.To support and to publish Jiang Fermat last theorem paper is prohibited in Academia Sinica. Remark. Chun-Xuan Jiang,A general proof of Fermat last theorem(Chinese),Mimeograph papers,July 1978. In this paper using circulant matrix,circulant determinant and permutation group theory Jiang had proved Fermat last theorem for odd prime exponent.
Category: Number Theory

[1] viXra:1103.0003 [pdf] submitted on 2 Mar 2011

Fermat Last Theorem Controversy (2)

Authors: Chun-Xuan Jiang
Comments: 7 pages.

The Fermat last theorem controversy is an argument between 20th century mathematicians Jiang Chun-Xuan(1992) and Andrew Wiles(1995) over who has first proved Fermat last theorem.
Category: Number Theory