[12] **viXra:1611.0410 [pdf]**
*submitted on 2016-11-30 07:48:39*

**Authors:** Zhang Tianshu

**Comments:** 18 Pages.

The ABC conjecture seemingly is difficult to carry conviction in the face of satisfactory many primes and satisfactory many odd numbers of 6K±1 from operational results of computer programs. So we select and adopt a specific equality 1+2N(2N-2)=(2N-1)2 with N≥2 satisfying 2N-1>(Rad(2N-2))1+ ε. Then, proceed from the analysis of the limits of values of ε to find its certain particular values, thereby finally negate the ABC conjecture once and for all.

**Category:** Number Theory

[11] **viXra:1611.0390 [pdf]**
*replaced on 2016-12-08 03:13:44*

**Authors:** Robert Deloin

**Comments:** 10 Pages. This is version 2 with important changes.

Bunyakovsky's conjecture states that under special conditions, polynomial integer functions of degree greater than one generate innitely
many primes.
The main contribution of this paper is to introduce a new approach that enables to prove Bunyakovsky's conjecture. The key idea of this new
approach is that there exists a general method to solve this problem by using only arithmetic progressions and congruences.
As consequences of Bunyakovsky's proven conjecture, three Landau's problems are resolved: the n^2+1 problem, the twin primes conjecture and
the binary Goldbach conjecture.
The method is also used to prove that there are infinitely many primorial and factorial primes.

**Category:** Number Theory

[10] **viXra:1611.0373 [pdf]**
*submitted on 2016-11-27 08:39:53*

**Authors:** Victor Christianto

**Comments:** 4 Pages. This paper will be submitted to Annals of Mathematics

In this paper we will give an outline of proof of Fermat’s Last Theorem using a graphical method. Although an exact proof can be given using differential calculus, we choose to use a more intuitive graphical method.

**Category:** Number Theory

[9] **viXra:1611.0224 [pdf]**
*submitted on 2016-11-14 18:05:57*

**Authors:** Jonas Kaiser

**Comments:** 11 Pages.

The sieve of Collatz is a new algorithm to trace back the non-linear Collatz problem to a linear cross out algorithm. Until now it is unproved.

**Category:** Number Theory

[8] **viXra:1611.0178 [pdf]**
*submitted on 2016-11-12 09:51:56*

**Authors:** Aaron Chau

**Comments:** 3 Pages.

十分幸运，本文应用的是永不改变的定律（多与少），而不再是重复那类受局限的定理。
感谢数学的美妙，因为多与少的个数区别永远会造成二个质数的距离= 2。简述，= 2。

**Category:** Number Theory

[7] **viXra:1611.0176 [pdf]**
*submitted on 2016-11-12 04:58:51*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In a previous paper I defined the notion of Harshad-Coman numbers as the numbers n with the property that (n – 1)/(s(n) – 1), where s(n) is the sum of the digits of n, is integer. In this paper I conjecture that there exist an infinity of even numbers n for which n^2 is a Harshad-Coman number and I also make a classification in four classes of all the even numbers.

**Category:** Number Theory

[6] **viXra:1611.0175 [pdf]**
*submitted on 2016-11-12 05:01:08*

**Authors:** Marius Coman

**Comments:** 3 Pages.

In a previous paper I defined the notion of Harshad-Coman numbers as the numbers n with the property that (n – 1)/(s(n) – 1), where s(n) is the sum of the digits of n, is integer. In this paper I conjecture that there exist an infinity of odd numbers n for which n^2 is a Harshad-Coman number and I also make a classification in three classes of all the odd numbers greater than 1.

**Category:** Number Theory

[5] **viXra:1611.0172 [pdf]**
*submitted on 2016-11-11 15:58:33*

**Authors:** Marius Coman

**Comments:** 2 Pages.

In this paper I make the following three conjectures: (I) If P is both a Poulet number and a Harshad number, than the number P – 1 is also a Harshad number; (II) If P is a Poulet number divisible by 5 under the condition that the sum of the digits of P – 1 is not divisible by 5 than P – 1 is a Harshad number; (III) There exist an infinity of Harshad numbers of the form P – 1, where P is a Poulet number.

**Category:** Number Theory

[4] **viXra:1611.0171 [pdf]**
*submitted on 2016-11-11 16:00:16*

**Authors:** Marius Coman

**Comments:** 2 Pages.

OEIS defines the notion of Harshad numbers as the numbers n with the property that n/s(n), where s(n) is the sum of the digits of n, is integer (see the sequence A005349). In this paper I define the notion of Harshad-Coman numbers as the numbers n with the property that (n – 1)/(s(n) – 1), where s(n) is the sum of the digits of n, is integer and I make the conjecture that there exist an infinity of Poulet numbers which are also Harshad-Coman numbers.

**Category:** Number Theory

[3] **viXra:1611.0120 [pdf]**
*submitted on 2016-11-09 07:22:21*

**Authors:** Jian Ye

**Comments:** 3 Pages.

Goldbach’s conjecture: symmetrical primes exists in natural numbers. the generalized Goldbach’s conjecture: symmetry of prime number in the former and tolerance coprime to arithmetic progression still exists.

**Category:** Number Theory

[2] **viXra:1611.0089 [pdf]**
*submitted on 2016-11-07 11:29:42*

**Authors:** W.B. Vasantha Kandasamy, K. Ilanthenral, Florentin Smarandache

**Comments:** 10 Pages.

The Collatz conjecture is an open conjecture in mathematics named so after Lothar Collatz who proposed it in 1937. It is also known as 3n + 1 conjecture, the Ulam conjecture (after Stanislaw Ulam), Kakutanis problem (after Shizuo
Kakutani) and so on. Several various generalization of the Collatz conjecture
has been carried. In this paper a new generalization of the Collatz conjecture
called as the 3n ± p conjecture; where p is a prime is proposed. It functions on
3n + p and 3n - p, and for any starting number n, its sequence eventually enters
a finite cycle and there are finitely many such cycles. The 3n ± 1 conjecture, is
a special case of the 3n ± p conjecture when p is 1.

**Category:** Number Theory

[1] **viXra:1611.0085 [pdf]**
*submitted on 2016-11-07 06:46:24*

**Authors:** Predrag Terzic

**Comments:** 32 Pages.

Some theorems and conjectures concerning prime numbers .

**Category:** Number Theory