Application of Bio-inspired Algorithms to the Cryptanalysis of Asymmetric Ciphers on the Basis of Composite Number

2021 ◽  
Author(s):  
Anastasiia V. Shoshina ◽  
Georgii I. Borzunov ◽  
Ekaterina Y. Ivanova
Keyword(s):  
Composite Number

THE KORSELT SET OF pq

2012 ◽  
Vol 08 (02) ◽  
pp. 299-309 ◽  
Author(s):  
OTHMAN ECHI ◽  
NEJIB GHANMI
Keyword(s):  
Positive Integer ◽  
Prime Divisor ◽  
Prime Numbers ◽  
Composite Number

Let α ∈ ℤ\{0}. A positive integer N is said to be an α-Korselt number (Kα-number, for short) if N ≠ α and N - α is a multiple of p - α for each prime divisor p of N. By the Korselt set of N, we mean the set of all α ∈ ℤ\{0} such that N is a Kα-number; this set will be denoted by [Formula: see text]. Given a squarefree composite number, it is not easy to provide its Korselt set and Korselt weight both theoretically and computationally. The simplest kind of squarefree composite number is the product of two distinct prime numbers. Even for this kind of numbers, the Korselt set is far from being characterized. Let p, q be two distinct prime numbers. This paper sheds some light on [Formula: see text].

scholarly journals Some More New Properties of Consecutive Odd Numbers

2017 ◽  
Vol 9 (5) ◽  
pp. 61
Author(s):  
Xingbo Wang
Keyword(s):  
Symmetric Distribution ◽  
Composite Number

The article proves several new properties of consecutive odd integers. The proved properties reveal divisors’ transition by subtracting two terms of an odd sequence, divisors’ stationary with adding or subtracting an item to the terms and pseudo-symmetric distribution of a divisor’s power in an odd sequence. The new properties are helpful for finding a divisor of an odd composite number in an odd sequence.

On the pseudoprimes of the form ax + b

1967 ◽  
Vol 63 (2) ◽  
pp. 389-392 ◽  
Author(s):  
A. Rotkiewicz
Keyword(s):  
Natural Number ◽  
Natural Numbers ◽  
Composite Number

A composite number n is called a pseudoprime if n|2n− 2.Theorem 1. If a and b are natural numbers such that (a, b) = 1, then there exist infinitely many pseudoprimes of the form ax + b, where x is a natural number.The proof of this theorem is given by the author in (5). This proof is based on the following two lemmas.

Now try this–in multiplication

1967 ◽  
Vol 14 (1) ◽  
pp. 47
Author(s):  
Charlotte W. Junge
Keyword(s):  
The Other ◽  
Composite Number

1. When the multiplier is a composite number: a) Separate the multiplier into 2 (or more) factors. b) Multiply the multiplicand by one of these factors, and that product by the other factor(s).

On the Number of False Witnesses for a Composite Number

1986 ◽  
Vol 46 (173) ◽  
pp. 259 ◽  
Author(s):  
Paul Erdos ◽  
Carl Pomerance
Keyword(s):  
Composite Number

scholarly journals Relation between Prime and Composite Number

BIBECHANA ◽  
2018 ◽  
Vol 1 ◽  
pp. 14-16
Author(s):  
Raju Ram Thapa
Keyword(s):  
Composite Number

This article was not peer-reviewed.No abstract available.

scholarly journals Elementary Number Theory Problems. Part II

2021 ◽  
Vol 29 (1) ◽  
pp. 63-68
Author(s):  
Artur Korniłowicz ◽  
Dariusz Surowik
Keyword(s):  
Number Theory ◽  
Positive Integer ◽  
Prime Numbers ◽  
Elementary Number Theory ◽  
Elementary Number ◽  
Composite Number

Summary In this paper problems 14, 15, 29, 30, 34, 78, 83, 97, and 116 from [6] are formalized, using the Mizar formalism [1], [2], [3]. Some properties related to the divisibility of prime numbers were proved. It has been shown that the equation of the form p 2 + 1 = q 2 + r 2, where p, q, r are prime numbers, has at least four solutions and it has been proved that at least five primes can be represented as the sum of two fourth powers of integers. We also proved that for at least one positive integer, the sum of the fourth powers of this number and its successor is a composite number. And finally, it has been shown that there are infinitely many odd numbers k greater than zero such that all numbers of the form 22 n + k (n = 1, 2, . . . ) are composite.

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