[PDF] a congruent to b (mod n)

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. The integer n is said to be the modulus. Lemma 1.2. If n is an integer, then a is congruent to b modulo n if and only if a and b have the same remainder when divided by n.
View PDF Document


  • What does a ? b mod n mean?

    For a positive integer n, two integers a and b are said to be congruent modulo n (or a is congruent to b modulo n), if a and b have the same remainder when divided by n (or equivalently if a ? b is divisible by n ). It can be expressed as a ? b mod n. n is called the modulus.

  • What does a ? b mod m mean?

    BASIC PROPERTIES OF CONGRUENCES. The letters a, b, c, d, k represent integers. The letters m, n represent positive integers. The notation a ? b (mod m) means that m divides a ? b. We then say that a is congruent to b modulo m.

  • What is an example of a congruent to b mod n?

    We say integers a and b are "congruent modulo n" if their difference is a multiple of n. For example, 17 and 5 are congruent modulo 3 because 17 - 5 = 12 = 4?3, and 184 and 51 are congruent modulo 19 since 184 - 51 = 133 = 7?19. We often write this as 17 ? 5 mod 3 or 184 ? 51 mod 19.
  • For a,b Œ G , we say a is congruent to b modulo H, written a? b(mod H), if and only ifab-1 Œ H . We will prove the following in class: Theorem: The relation a? b(mod H) is an equivalence relation. As you may have noticed, the notation is reminiscent of that used for the integers modulo. n.
View PDF Document




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





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