[PDF] Discrete Mathematics Chapter 4: Number Theory and Cryptography





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3 Congruence

Definition 3.1 If a and b are integers and n > 0 we write a ? b mod n to mean n



3 Congruence

Definition 3.1 If a and b are integers and n > 0 we write a ? b mod n to mean n



Divisibility Memorize: If a and b are integers we say that a divides b

b ? and the remainder r is a(mod b) integer between 0 and b ? 1 then the notation (dkdk?1 ...d1d0)b means dk × bk + dk?1 × bk?1 + .



Congruence and Congruence Classes

The next definition yields another example of an equivalence relation. Definition 11.2. Let a b



DIVISIBILITÉ ET CONGRUENCES

Définition : Soit a et b deux entiers relatifs. a divise b s'il existe un entier relatif k tel que b = ka. On dit également : - a est un diviseur de b.



Solutions to Homework Set 3 (Solutions to Homework Problems

If a b are integers such that a ? b (mod p) for every positive prime p



Math 110 Homework 1 Solutions

15 janv. 2015 1. (a) Define the phrase m divides n. (b) Given integers m and n state the definition of the greatest common divisor of ...





Discrete Mathematics Chapter 4: Number Theory and Cryptography

Definition. If a and b are integers and m is a positive integer then a is congruent to b modulo m iff m



3. Equivalence Relations 3.1. Definition of an Equivalence Relations

The relation a ? b(mod m) is an equivalence relation on the set of integers. Page 5. 3. EQUIVALENCE RELATIONS. 37. Proof. Reflexive. If a 

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