[13] **viXra:1012.0047 [pdf]**
*submitted on 23 Dec 2010*

**Authors:** Chun-Xuan Jiang

**Comments:** 95 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
J_{2}(ω) we prove that the new prime theorems (841)-(890) contain infinitely many prime
solutions and no prime solutions. From (6) we are able to find the smallest solution
(see paper). This is the Book theorem.

**Category:** Number Theory

[12] **viXra:1012.0036 [pdf]**
*submitted on 15 Dec 2010*

**Authors:** Mohd Shukri Abd Shukor

**Comments:** 30 pages

A new approach in deriving Sum of Power series using reverse look up method, a
method where a mathematical formulation is constructed from set of data. Faulhaber [1]
derived a general equation for Power sums and calculated the terms up to (Part V)

**Category:** Number Theory

[11] **viXra:1012.0035 [pdf]**
*submitted on 15 Dec 2010*

**Authors:** Mohd Shukri Abd Shukor

**Comments:** 19 pages

A new approach in deriving Sum of Power series using reverse look up method, a ,method where
a mathematical formulation is constructed from set of data. Faulhaber [1] derived a general equation for
Power sums and calculated the terms up to (Part IV)

**Category:** Number Theory

[10] **viXra:1012.0034 [pdf]**
*submitted on 15 Dec 2010*

**Authors:** Mohd Shukri Abd Shukor

**Comments:** 19 pages

An extension of Sum of Power formulation into alternating system. The general
formulation is given as follows:

**Category:** Number Theory

[9] **viXra:1012.0033 [pdf]**
*submitted on 15 Dec 2010*

**Authors:** Mohd Shukri Abd Shukor

**Comments:** 18 pages

Sums of Power mainly deal with positive integer power p (i.e. p ε^{+} Z). In this paper, I
would like to show that the sums of power that I had formulated in paper part I [1] also can be
applied to the non-integer power p. The sums of power for positive non-integers (i.e. SPPNI) in
this paper still adopting the same general sums of power formulation. However, the value of m has
no bound and it is used as precision control. The larger the value of m used, the more accuracy the
result would be.

**Category:** Number Theory

[8] **viXra:1012.0032 [pdf]**
*replaced on 19 Nov 2011*

**Authors:** Mohd Shukri Abd Shukor

**Comments:** 47 pages

Sum of Power had gathered interest of many classical mathematicians for more than two thousand
years ago. The quests of finding sum of power or discrete sum of numerical power can be traced back
from the time of Archimedes in third BC then to Faulhaber in the sixteen century. Until today there is
no closed form sums of power formulation for an arithmetic progression has been found. Many
mathematicians were involved in this research and many approaches have been introduced but none is
found to be conclusive. The generalized equation for sums of power discovered in this research has
been compared to Faulhaber's sums of power for integers and it is found that this new generalized
equation can be used for both integers and arithmetic progression, thus offering a new frontier in
studying symmetric function, Fermat's last theorem, Riemman's Zeta function etc.

**Category:** Number Theory

[7] **viXra:1012.0022 [pdf]**
*replaced on 9 Jan 2011*

**Authors:** Chun-Xuan Jiang

**Comments:** 24 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." (part 6)

**Category:** Number Theory

[6] **viXra:1012.0021 [pdf]**
*replaced on 9 Jan 2011*

**Authors:** Chun-Xuan Jiang

**Comments:** 25 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." (part 5)

**Category:** Number Theory

[5] **viXra:1012.0010 [pdf]**
*replaced on 9 Jan 2011*

**Authors:** Chun-Xuan Jiang

**Comments:** 27 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." (part 4)

**Category:** Number Theory

[4] **viXra:1012.0009 [pdf]**
*replaced on 9 Jan 2011*

**Authors:** Chun-Xuan Jiang

**Comments:** 25 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." (part 3)

**Category:** Number Theory

[3] **viXra:1012.0008 [pdf]**
*replaced on 9 Jan 2011*

**Authors:** Chun-Xuan Jiang

**Comments:** 25 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." (part 2)

**Category:** Number Theory

[2] **viXra:1012.0007 [pdf]**
*replaced on 12 Jan 2011*

**Authors:** Chun-Xuan Jiang

**Comments:** 27 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." (part 1)

**Category:** Number Theory

[1] **viXra:1012.0004 [pdf]**
*submitted on 2 Dec 2010*

**Authors:** Tong Xin Ping

**Comments:** 6 pages, in Chinese

This paper is to discuss the six details in the Hardy-Littlewood Conjecture (A):...

**Category:** Number Theory