ax=b mod n

PDF	Chapitre 3 : congruences et arithmétique modulaire La condition que d divise b est nécessaire c'est à dire si la congruence a une solution alors d divise b En effet si on a ax ≡ b (mod n) alors il existe

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Comment Ecrire congruence ?
2/ Congruence : définition
On dit que « a est congru à b modulo n » ou que « a et b sont congrus modulo n » si : a et b ont le même reste dans la division euclidienne par n.
Comment Etudier la congruence modulo n ?
Pour comprendre les congruences, nous avons besoin d'un entier naturel non nul n, et de deux entiers relatifs a et b.
Si a – b est divisible par n, on dit que a et b sont congrus modulo n et on note a ≡ b [n].
On dit aussi que a est congru à b modulo n.
Exemple : 15 ≡ 7 [4] car 15 – 7 = 8, qui est divisible par 4.
Deux nombres entiers sont dits congrus modulo n si leur différence est un multiple de n, n étant un nombre entier.
On peut aussi dire que deux nombres entiers sont dits congrus modulo n s'ils ont même reste par leur division euclidienne par n.

Qu'est-ce que la notion de congruence ?

Fait de coïncider, de s'ajuster parfaitement. 2.
Qualité d'une articulation ou d'une anastomose dont les deux parties s'adaptent parfaitement.

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