Quiz interactif : Maîtrisez les nombres entiers et l'arithmétique

Question 1 sur 10 10:00

[{"id":74382,"question":"Quel est le plus grand commun diviseur (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 = 2×28 et 98 = 2×49, puis 28 et 49 sont premiers entre eux.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74383,"question":"Si a ≡ 3 [7] et b ≡ 5 [7], alors a + b ≡ ? [7]","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"a + b ≡ 3 + 5 ≡ 8 ≡ 1 [7], donc l'affirmation est fausse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74384,"question":"Quel théorème permet de résoudre l'équation 7x + 11y = 1 ?","option_a":"Théorème de Gauss","option_b":"Théorème de Bézout","option_c":"Théorème de Fermat","option_d":"Théorème de Pythagore","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le théorème de Bézout stipule que si a et b sont premiers entre eux, alors il existe des entiers x et y tels que ax + by = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74385,"question":"Si n est un entier divisible par 3 et par 5, alors n est divisible par :","option_a":"2","option_b":"15","option_c":"8","option_d":"12","option_e":"","option_f":"","bonne_reponse":"B","explication":"Si n est divisible par 3 et 5, et que 3 et 5 sont premiers entre eux, alors n est divisible par 3×5 = 15.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74386,"question":"L'équation 4x + 6y = 2 admet-elle des solutions entières ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'équation admet des solutions car 4 et 6 sont divisibles par 2, et 2 est aussi divisible par 2. Les solutions sont de la forme x = -1 + 3k et y = 1 - 2k pour tout entier k.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74387,"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":"D","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":74388,"question":"Si a ≡ 2 [5] et b ≡ 3 [5], alors a × b ≡ ? [5]","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"a × b ≡ 2 × 3 ≡ 6 ≡ 1 [5], donc l'affirmation est fausse.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74389,"question":"Quel est le plus petit entier positif x tel que 3x ≡ 1 [7] ?","option_a":"1","option_b":"2","option_c":"5","option_d":"7","option_e":"","option_f":"","bonne_reponse":"C","explication":"3×5 = 15 ≡ 1 [7], donc x = 5 est la solution.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74390,"question":"Si a et b sont deux entiers premiers entre eux, alors a² et b² sont aussi premiers entre eux.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Si a et b sont premiers entre eux, alors a² et b² le sont aussi, car tout diviseur commun de a² et b² divise a et b.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74391,"question":"Quel est le PGCD de 120 et 180 ?","option_a":"30","option_b":"60","option_c":"90","option_d":"120","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le PGCD de 120 et 180 est 60, car 120 = 2³×3×5 et 180 = 2²×3²×5, donc le PGCD est 2²×3×5 = 60.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]