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

**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 = m^{2}. '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 = k^{2} [4]
equation and asked to find solutions for them.

**Category:** Number Theory

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

**Authors:** Chun-Xuan Jiang

**Comments:** 6 pages.

In this paper we prove *R ^{n}* =

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

**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]**
*submitted on 21 Mar 2011*

**Authors:** Martiros Khurshudyan

**Comments:** 3 pages.

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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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