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 J2(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) Rn = y15 y25

Authors: Chun-Xuan Jiang
Comments: 4 pages.

In this paper we prove Rn = y15 y25 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 d2 = a3 + c5 and d2 = a3 + c7 have infinitely many coprime integer solutions.
Category: Number Theory