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

**Authors:** Andrew Nassif

**Comments:** 5 Pages.

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

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

**Authors:** Julien Laurendeau

**Comments:** 2 Pages.

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

**Category:** Number Theory

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

**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

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

**Authors:** Marius Coman

**Comments:** 5 Pages.

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

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

**Authors:** Edigles Guedes

**Comments:** 1 page

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

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

**Authors:** Edigles Guedes

**Comments:** 5 pages

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

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

**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

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

**Authors:** Marius Coman

**Comments:** 2 Pages.

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

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

**Authors:** Olivier Massot

**Comments:** 85 Pages.

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

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

**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

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

**Authors:** Edigles Guedes

**Comments:** 9 pages

We developed some formulas to represent integer numbers as the sum of cube roots.

**Category:** Number Theory

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

**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

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

**Authors:** Marius Coman

**Comments:** 4 Pages.

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

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

**Authors:** Marius Coman

**Comments:** 3 Pages.

I wrote an article entitled “A formula for generating primes and a possible infinite series of Poulet numbers”; the sequence I was talking about not only that is, indeed, infinite, but is also already known as the sequence of Cipolla pseudoprimes to base 2. Starting from comparing Cipolla pseudoprimes and some of my notes I discovered a new class of pseudoprimes.

**Category:** Number Theory

[1] **viXra:1304.0001 [pdf]**
*submitted on 2013-04-01 07:39:56*

**Authors:** Predrag Terzic

**Comments:** 2 Pages.

Polynomial time prime testing algorithms for specific classes of Proth numbers are introduced

**Category:** Number Theory