[PDF] CHAPITRE 3 : CONGRUENCES ET ARITHMÉTIQUE MODULAIRE
Soit p premier et a entier avec a ≡ 0 (mod p) Alors pour tout c il existe une solution x de la congruence ax ≡ c (mod p), et cette solution est unique modulo p
[PDF] 3 Congruence
A simple consequence is this: Any number is congruent mod n to its remainder when divided by n For if a = nq + r, the above result shows that a ≡ r mod n Thus
[PDF] Congruences
In general, we call the set of all integers congruent to a given integer a mod n a congruence class mod n It is easy to see that the number of congruence classes
[PDF] DIVISIBILITÉ ET CONGRUENCES - maths et tiques
On dit que 21 et 6 sont congrus modulo 5 Deux entiers a et b sont congrus modulo n lorsque a – b est divisible par n On note Démontrer une congruence :
[PDF] Congruences, applications
Exercice 6 14 — Donnez la congruence modulo 18 de 1823242 puis celle de 2222321 modulo 20 Exercice 6 15 — Montrez que n7 ≡ n mod 42
[PDF] LECTURE 3: CONGRUENCES 1 Basic properties of congruences
We say that a is not congruent to b modulo m, and write a ≡ b (mod m), when m ( a − b) Theorem 1 2 Let a, b, c, d be integers Then (i) a ≡ b (mod m) ⇐⇒ b
[PDF] Congruences - Mathtorontoedu
third number m, then we say "a is congruent to b modulo m", and write a ≡ b Theorem 1: Every integer is congruent ( mod m) to exactly one of the numbers in
[PDF] Congruence and Congruence Classes
The next definition yields another example of an equivalence relation Definition 11 2 Let a, b, n ∈ Z with n > 0 Then a is congruent to b modulo n; a ≡ b (mod n)
[PDF] Cours dintroduction `a larithmétique - Normale Sup
8 mar 2014 · On dit que a est congruent `a b modulo N s'il a le même reste que b `a la division par N Dans ce cas on note a ≡ b (mod N) Théor`eme 1
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