# a 22 Integers 14 ( 2014 ) a Density Chinese Remainder Theorem
نویسنده
چکیده
Given collections A and B of residue classes modulo m and n, respectively, we investigate conditions on A and B that ensure that, for at least some (a, b) 2 A⇥B, the system: x ⌘ a mod m and x ⌘ b mod n has an integer solution, and we quantify the number of such admissible pairs (a, b). The special case where A and B consist of intervals of residue classes has application to the Lonely Runner Conjecture.
منابع مشابه
Modular Integer Arithmetic 1 Christoph Schwarzweller Institute of Computer
In this article we show the correctness of integer arithmetic based on Chinese Remainder theorem as described e.g. in [11]: Integers are transformed to finite sequences of modular integers, on which the arithmetic operations are performed. Retransformation of the results to the integers is then accomplished by means of the Chinese Remainder theorem. The method presented is a typical example for...
متن کاملCourse 311: Michaelmas Term 2005 Part I: Topics in Number Theory
1 Topics in Number Theory 2 1.1 Subgroups of the Integers . . . . . . . . . . . . . . . . . . . . 2 1.2 Greatest Common Divisors . . . . . . . . . . . . . . . . . . . . 2 1.3 The Euclidean Algorithm . . . . . . . . . . . . . . . . . . . . . 3 1.4 Prime Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.5 The Fundamental Theorem of Arithmetic . . . . . . . . . . . . 5 1.6 The Infini...
متن کاملKineski teorem o ostatcima za polinome
We start by giving a brief description of the classical Chinese remainder theorem for integers, after whichwe define the greatest common divisor of two polynomials and congruences modulo a polynomial. These concepts allow us to state and prove the Chinese remainder theorem for polynomials. After presenting some important consequences of that theorem, we give its applications to the factorizatio...
متن کاملCourse Ma2c03, Hilary Term 2014 Section 9: Introduction to Number Theory and Cryptography
9 Introduction to Number Theory 168 9.1 Subgroups of the Integers . . . . . . . . . . . . . . . . . . . . 168 9.2 Greatest Common Divisors . . . . . . . . . . . . . . . . . . . . 168 9.3 The Euclidean Algorithm . . . . . . . . . . . . . . . . . . . . . 169 9.4 Prime Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . 172 9.5 The Fundamental Theorem of Arithmetic . . . . . . . . . . . . ...
متن کاملTo Design and Implement Novel Method of Encryption using Modified RSA and Chinese Remainder Theorem
Security can only be as strong as the weakest link. In this world of cryptography, it is now well established, that the weakest link lies in the implementation of cryptographic algorithms. This paper deals with RSA algorithm with and without Chinese Remainder Theorem. In practice, RSA public exponents are chosen to be small which makes encryption and signature verification reasonably fast. Priv...
متن کامل