# Number Theory

## 1304 Submissions

 viXra:1304.0163 [pdf] replaced on 2013-06-21 16:10:42

### P vs. NP and Riemann Hypothesis Solution (Revised)

Authors: Andrew Nassif

This problem has been solved by me over a year ago, and published. Today I am posting a more complex and complicated version, yet put in Layman terms. I hope by doing this it will garner the attention of Clay Mathematics as well as show logical input on its mathematical endeavors. Solving and coming up with a proof of the Riemann Hypothesis can lead to a change in computational mathematics, number theory, set theory, and logic ofcourse. The same goes to the P vs. NP.
Category: Number Theory

 viXra:1304.0160 [pdf] submitted on 2013-04-29 05:33:34

### Observation on Fermat's Last Theorem

Authors: Julien Laurendeau

In this paper, we are discovering something that looks a lot like Fermat's last theorem.
Category: Number Theory

 viXra:1304.0104 [pdf] replaced on 2013-04-22 22:15:14

### Primes in the Intervals [kn,(k+1)n]

Authors: S. Sambasivarao
Comments: 4 Pages. This paper is communicated to "Notes on Number Theory and Discrete Mathematics"

Abstract. In this paper, we prove: (a) for every integer n > 1 and a fixed integer k less than or equal to n, there exists a prime number p in between kn and (k + 1)n, and (b) conjectures of Legendre, Oppermann, Andrica, Brocard, and Improved version of Legendre conjecture as a particular case of (a).
Category: Number Theory

 viXra:1304.0092 [pdf] submitted on 2013-04-19 01:58:17

### Connections Between the Three Prime Factors of 3-Carmichael Numbers

Authors: Marius Coman

It was always obvious to me that, beside Korselt’s criterion, that gives a relation between any prime factor of a Carmichael number and the number itself, there must be a relation between the prime factors themselves; here I present a conjecture on the Carmichael numbers with three prime factors expressing the larger two prime factors as a function of the smallest one and few particular cases of connections between all three prime factors.
Category: Number Theory

 viXra:1304.0090 [pdf] submitted on 2013-04-18 18:20:37

### Some Identities Involving four Squares II

Authors: Edigles Guedes

ABSTRACT. We continue to develop some algebraic identities related to the power three as: (a^2 c^2+a^2 d^2+b^2 c^2+b^2 d^2 )^3=[ac(a^2-3b^2 )(c^2-3d^2 )]^2+[ad(a^2-3b^2 )(3c^2-d^2 )]^2+[bc(3a^2-b^2 )(c^2-3d^2 )]^2+[bd(3a^2-b^2 )(3c^2-d^2 )]^2.
Category: Number Theory

 viXra:1304.0083 [pdf] submitted on 2013-04-17 12:50:46

### Some Algebraic Identities Involving four Square

Authors: Edigles Guedes

ABSTRACT. We have developed some algebraic identities related to power three as: 4〖(a^2 c^2+a^2 d^2+b^2 c^2+b^2 d^2)〗^3=[(a+b)(a^2-4ab+b^2 )(c+d)(c^2-4cd+d^2 )]^2+[(a+b)(a^2-4ab+b^2 )(c-d)(c^2+4cd+d^2 )]^2+[(a-b)(a^2+4ab+b^2 )(c+d)(c^2-4cd+d^2 )]^2+[(a-b)(a^2+4ab+b^2 )(c-d)(c^2+4cd+d^2 )]^2.
Category: Number Theory

 viXra:1304.0070 [pdf] replaced on 2014-04-11 06:56:26

### Search for Fermat's Proof

Authors: Ahmed Idrissi Bouyahyaoui
Comments: 3 Pages. French and abstract in Englih

Search for Fermat's proof : (X, Y, Z, n) є N+^4 , X^n + Y^n = Z^n ==> x= X+Y-Z, u, v є N+ , w=u+v, Pn(x)=(x+u)^n+(x+v)^n-(x+w)^n (X, Y, Z) є N+^3 , X^4 + Y^4 ≠ Z^4 ==> (Z-Y)(Z-X) irrational (Z-Y)(Z-X) irrational ==> (X, Y, Z, n) є N+^4 , X^n + Y^n ≠ Z^n
Category: Number Theory

 viXra:1304.0061 [pdf] submitted on 2013-04-13 20:06:44

### An Interesting and Unexpected Property of Carmichael Numbers and a Question

Authors: Marius Coman

I was researching a kind of generalized Cunningham chains that generate, instead of primes, Fermat pseudoprimes to some base when purely by chance I noticed a property of absolute Fermat pseudoprimes, equally interesting and unexpected. By a childish simple operation, a new class of numbers is obtained from Carmichael numbers.
Category: Number Theory

 viXra:1304.0060 [pdf] replaced on 2014-04-18 03:58:34

### Goldbach, Legendre, Brocard, Considérations élémentaires Sur Quelques Conjectures.

Authors: Olivier Massot

Symmetry proves to be a useful concept when it comes to studying some conjectures in Number theory. This study (in french) concentrates on three already well-known conjectures and the following one: For any given prime number p, there exists at least one prime number in each and every interval [kp,(k+1)p[, where k is a non-zero integer that is less than or equal to p.
Category: Number Theory

 viXra:1304.0058 [pdf] replaced on 2013-04-18 04:34:26

### Le Théorème de Fermat-Wiles et le Critère de Eisenstein

Authors: Ahmed Idrissi Bouyahyaoui
Comments: 4 Pages. Summary is in English and article is in French.

Let P(X) a polynomial associated to the Fermat's equation x^p+y^p-z^p=0 (p is an odd prime number) and R(X) its reduction modulo k (k is a prime number): R(X)= P(X) [k]. R(X) is irreducible (Eisenstein criterion) and, therefore, P(X) is irreducible. P(X) being irreducible, it hasn't integer roots and so the associated equation x^p+y^p-z^p=0 hasn't nonzero integer solutions for all odd prime number p.
Category: Number Theory

 viXra:1304.0045 [pdf] submitted on 2013-04-09 17:15:40

### On the Representation of Integer Numbers by the Sum of Cube Roots

Authors: Edigles Guedes

We developed some formulas to represent integer numbers as the sum of cube roots.
Category: Number Theory

 viXra:1304.0020 [pdf] replaced on 2017-06-14 09:38:27

### Talent's Error

Authors: Liu Ran
Comments: 7 Pages. add condition of nature number neither being a prime nor a composite number.

both experiment and logic analyze have demonstrate Euclid's proof is wrong
Category: Number Theory

 viXra:1304.0017 [pdf] submitted on 2013-04-04 08:30:26

### Four Conjectures Regarding Fermat Pseudoprimes and Few Known Types of Pairs of Primes

Authors: Marius Coman

There are already known some relations between Fermat pseudoprimes and the pairs of primes [p, 2p – 1]. We will here show few relations between Fermat pseudoprimes and the pairs of primes of the type [p, 2p – 1], [p, 2p + 1], [p, sqrt(2p – 1)], respectivelly [p, k*p – k + 1].
Category: Number Theory

 viXra:1304.0009 [pdf] submitted on 2013-04-02 08:06:05

### A New Class of Fermat Pseudoprimes and Few Remarks About Cipolla Pseudoprimes

Authors: Marius Coman