[10] **viXra:1402.0165 [pdf]**
*submitted on 2014-02-26 19:24:20*

**Authors:** Ihsan Raja Muda Nasution

**Comments:** 1 Page.

We just use a certain algorithmic procedure to
eliminate the critical line from the complex plane.
As the result, we obtain a disproof of the Riemann
hypothesis in a simple manner.

**Category:** Number Theory

[9] **viXra:1402.0159 [pdf]**
*submitted on 2014-02-25 20:02:48*

**Authors:** Zhang Tianshu

**Comments:** 10 Pages.

In this article, we will prove the Beal’s conjecture by certain usual mathematical fundamentals with the aid of proven Fermat’s last theorem, and finally reach a conclusion that the Beal’s conjecture is tenable.

**Category:** Number Theory

[8] **viXra:1402.0128 [pdf]**
*submitted on 2014-02-19 09:37:38*

**Authors:** Marius Coman

**Comments:** 2 Pages.

Obviously, like everyone fond of arithmetic, I always dreamed to discover formulas to generate only primes; unfortunately, during the time, I dropped somewhat to find this Holy Grail. I found out that there are formulas that generate only primes, like Rowland’s formula, but often these formulas haven’t the desired impact, because, for instance, the value of the numbers used as “input” is larger than the one of the primes obtained as “output” and so on. In this paper I present a very simple formula based on Smarandache function, which, using primes of a certain form, conducts often to larger primes and products of very few primes and I also make four conjectures.

**Category:** Number Theory

[7] **viXra:1402.0122 [pdf]**
*submitted on 2014-02-18 07:32:10*

**Authors:** Ren Yongxue1 ; Ren Yi 2

**Comments:** 11 Pages.

the paper methods of proof goldbach conjecture equations of （a+b）=2√A1， in quadrant I n d space coordinate system, demonstrate the sum of any two real Numbers (a + b) is equal to the NTH power by the sum of the two real Numbers (a + b) for a quarter of a square of side area of the square root of 2 times the NTH power. N scope is: n p 0 n ∈ n (positive integer infinite set)

**Category:** Number Theory

[6] **viXra:1402.0119 [pdf]**
*submitted on 2014-02-18 11:52:11*

**Authors:** Marius Coman

**Comments:** 3 Pages.

In one of my previous papers, “An ordered set of certain seven numbers that results constantly from a recurrence formula based on Smarandache function”, combining two of my favorite topics of study, the recurrence relations and the Smarandache function, I discovered that the formula f(n) = S(f(n – 2)) + S(f(n – 1)), where S is the Smarandache function and f(1), f(2) are any given different non-null positive integers, seems to lead every time to a set of seven values (i.e. 11, 17, 28, 24, 11, 15, 16) which is then repeating infinitely. In this paper I show few other interesting patterns based on recurrence and Smarandache function and I define the Smarandache-Coman constants.

**Category:** Number Theory

[5] **viXra:1402.0088 [pdf]**
*submitted on 2014-02-13 14:08:04*

**Authors:** Marius Coman

**Comments:** 3 Pages.

I treated the 2-Poulet numbers in many papers already but they continue to be a source of inspiration for me; in this paper I make two conjectures on primes inspired by the relation between the prime factors of a 2-Poulet number and I also make a conjecture on Fermat pseudoprimes to base two.

**Category:** Number Theory

[4] **viXra:1402.0073 [pdf]**
*submitted on 2014-02-10 07:00:37*

**Authors:** Marius Coman

**Comments:** 2 Pages.

Combining two of my favourite objects of study, the Fermat pseudoprimes and the Smarandache function, I was able to formulate a criterion, inspired by Korselt’s criterion for Carmichael numbers and by Smarandache function, which seems to be necessary (though not sufficient as the Korselt’s criterion for absolute Fermat pseudoprimes) for a composite number (without a set of probably definable exceptions) to be a Fermat pseudoprime to base two.

**Category:** Number Theory

[3] **viXra:1402.0030 [pdf]**
*submitted on 2014-02-04 05:51:32*

**Authors:** John Frederick Sweeney

**Comments:** 12 Pages. includes graphics

The Euler e is a natural logarithm from which matter begins. Now, in Vedic Physics, it would appear that matter develops along the range of Phi, or the Golden Section, which forms the border between the 8 x 8 and 9 x 9 states of matter. Therefore, Phi would form the exterior of any object formed completely of one state of matter, and the border between the two states of any object formed of two states of matter. The third state of matter is invisible to us, and known generally in world cultures by the concept of “hell,” which is a misnomer and which represents a serious misunderstanding of Vedic science. We can know its general proportions by reflecting from positive Phi values into the Thaasic zone from the 8 x 8 Satwa or 9 x 9 Raja zones. This paper presents values for all of these zones, and shows how the euler logarithm is built into the Great Pyramid at Giza.

**Category:** Number Theory

[2] **viXra:1402.0029 [pdf]**
*submitted on 2014-02-04 06:04:17*

**Authors:** Wenceslao Segura González

**Comments:** 8 Pages. Spanish

We formulate and prove a theorem that allows us to establish the analytical function of an application between integer numbers that is closely linear. The theorem is widely used in Calendarists calculations, especially in converting dates from one calendar to another. In the second part of this research we apply the theorem to several specific cases that appear in the theory of the calendars.

**Category:** Number Theory

[1] **viXra:1402.0003 [pdf]**
*replaced on 2014-02-03 01:35:50*

**Authors:** Marius Coman

**Comments:** 2 Pages.

Studying the two well known recurrent relations with the exceptional property that they generate only values which are equal to 1 or are odd primes, id est the formula which belongs to Eric Rowland and the one that belongs to Benoit Cloitre, I managed to discover a formula based on Smarandache function, from the same family of recurrent relations, which, instead to give a prime value for any input, seems to give the same value, 2, if and only if the value of the input is an odd prime; also, for any value of input different from 1 and different from an odd prime, the value of output is equal to n + 1. I name this relation the Coman-Smarandache criterion for primality and the exceptions from this rule, if they exist, Coman-Smarandache pseudoprimes.

**Category:** Number Theory