# Number Theory

## 1104 Submissions

[3] **viXra:1104.0057 [pdf]**
*submitted on 19 Apr 2011*

### The Proofs of Binary Goldbach’s Theorem Using Only Partial Primes

**Authors:** Chun-Xuan Jiang

**Comments:** 21 pages.

In 1994 we discovered the new arithmetic function
*J*_{2}(*ω*). Using it we proved
the binary Goldbach’s theorem [1]. In this chapter
we yield the more detailed proofs of the binary
Goldbach’s theorem using only partial primes.

**Category:** Number Theory

[2] **viXra:1104.0011 [pdf]**
*replaced on 8 Apr 2011*

### Generalized Fermat’s Last Theorem (3) *R*^{n} = *y*_{1}^{5 } − *y*_{2}^{5}

**Authors:** Chun-Xuan Jiang

**Comments:** 4 pages.

In this paper we prove
*R*^{n} = *y*_{1}^{5
} − *y*_{2}^{5} has no
nonzero integer solutions for n ≥ 2. In 1978 using
this method we had proved Fermat’s last theorem [1].
But on the afternoon of July 19, 1978 this proof was
disproved by Chinese mathematics institute of Academia
Sinica. How tragic!

**Category:** Number Theory

[1] **viXra:1104.0010 [pdf]**
*submitted on 5 Apr 2011*

### Fermat-Catalan Equations (1)

**Authors:** Chun-Xuan Jiang

**Comments:** 4 pages.

In this paper we prove that Fermat-Catalan equations
*d*^{2} = *a*^{3} + *c*^{5} and
*d*^{2} = *a*^{3} + *c*^{7} have
infinitely many coprime integer solutions.

**Category:** Number Theory