maths urgent congruences


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PDF NOMBRES ENTIERS ET RATIONNELS CONGRUENCES

L'ex- pression allemande « der liebe Gott » ne sous-entend pas une vision mystique des mathématiques pas plus que l'expression française « le Bon Dieu » Page 

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rédiger ou raisonner en mathématiques ne signifie pas grand chose de précis et ne semble pas important Proposition 4 (Propriétés des congruences) 92 Page 

PDF 1 Les congruences

Ces questions sont à l'origine de la notion de congruence et plus généralement de l'arithmétique modulaire D'une manière générale pour l'étude des congruences 

PDF Congruences et théorème chinois des restes

Ce théorème est très important pour les codes secrets La réciproque est fausse (nombres de Carmichael) [a 560 ≡ 1 (mod 561) hors 561 = 3 × 11 × 17]

PDF Chapitre 2

Il est important de voir comment les opérations usuelles se comportent avec les congruences Est-il possible d'additionner ou multiplier des congruences?

  • Comment démontrer une congruence ?

    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 ?

    Propriété : Soit n un entier naturel non nul.
    Deux entiers a et b sont congrus modulo n, si et seulement si, la division euclidienne de a par n a le même reste que la division euclidienne de b par n.
    Comme a ≡ b n⎡⎣⎤⎦, a – b est divisible par n et donc r – r' est divisible par n.

  • Comment calculer les congruence ?

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

Dans une addition ou une soustraction, on peut remplacer un nombre par autre qui lui égal modulo [n]. Autrement dit: Si a≡b [n] et c≡d [n] alors a+c≡b+d [n].Autres questions
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