Quiz : Maîtrisez l'arithmétique des entiers en Terminale !

Question 1 sur 10 10:00

[{"id":71482,"question":"Quel est le PGCD de 56 et 98 ?","option_a":"12","option_b":"14","option_c":"16","option_d":"18","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le PGCD de 56 et 98 est 14, car 56 = 14 × 4 et 98 = 14 × 7, et 4 et 7 sont premiers entre eux.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71483,"question":"Deux entiers a et b sont premiers entre eux si et seulement si leur PGCD est égal à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est vrai : par définition, deux entiers sont premiers entre eux si leur PGCD est 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71484,"question":"Quel est le reste de la division de 1234 par 7 ?","option_a":"2","option_b":"3","option_c":"4","option_d":"5","option_e":"","option_f":"","bonne_reponse":"C","explication":"1234 ÷ 7 = 176 avec un reste de 2, car 7 × 176 = 1232 et 1234 - 1232 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71485,"question":"Si a ≡ b [n] et b ≡ c [n], alors a ≡ c [n].","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est vrai : la relation de congruence est transitive.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71486,"question":"Quel est le PPCM de 12 et 18 ?","option_a":"24","option_b":"36","option_c":"48","option_d":"72","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le PPCM de 12 et 18 est 36, car 36 est le plus petit multiple commun à 12 et 18.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71487,"question":"Le théorème de Gauss permet de simplifier une équation du type au + bv = c.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"C'est vrai : le théorème de Gauss est utilisé pour résoudre des équations diophantiennes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71488,"question":"Quel est le nombre de solutions de l'équation 3x ≡ 5 [7] ?","option_a":"0","option_b":"1","option_c":"2","option_d":"3","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'équation 3x ≡ 5 [7] a une unique solution modulo 7, car 3 et 7 sont premiers entre eux.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71489,"question":"Si a divise b et b divise c, alors a divise c.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est vrai : la divisibilité est une relation transitive.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71490,"question":"Quel est le dernier chiffre de 7^2024 ?","option_a":"1","option_b":"3","option_c":"7","option_d":"9","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les puissances de 7 ont un cycle de 4 : 7, 9, 3, 1. 2024 mod 4 = 0, donc le dernier chiffre est 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":71491,"question":"Si a ≡ b [n], alors a^k ≡ b^k [n] pour tout entier k ≥ 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est vrai : la congruence est compatible avec l'élévation à une puissance.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]