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

Congruence and Congruence Classes

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

Problem Set 4 Solutions

22 févr. 2005 Solution. The statement a ? b (mod n) implies n (a ? b) which means there is an integer k such that nk = ...

Congruences and Modular Arithmetic

Then congruence modulo n is an equivalence relation on Z. Proof (Sketch). Let ab

0

Congruences

Suppose n is a fixed integer. We will say that two integers a and b are congruent modulo n and we write a ? b mod n if a ? b is divisible by n.

CHAPITRE 3 : CONGRUENCES ET ARITHMÉTIQUE MODULAIRE

a ? 0 (mod n) ?? a = nk avec k entier. ?? a est un multiple de n. Quelques propriétés de la congruence. Théorème 1.2. Soit a b

1 p. 61 #26 Prove that the congruence ax = b (mod n) has a solution

and only if d = (a n) divides b. If d b

BASIC PROPERTIES OF CONGRUENCES The letters a b

d

1 Congruence and modular arithmetics

Let a b