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Question 1 sur 10 10:00

[{"id":5755,"question":"Si a et b sont deux entiers tels que a divise b, alors :","option_a":"a \u003E b","option_b":"b est un multiple de a","option_c":"a et b sont premiers entre eux","option_d":"a = b","option_e":"","option_f":"","bonne_reponse":"B","explication":"Si a divise b, alors il existe un entier k tel que b = a × k. Ainsi, b est un multiple de a.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":5756,"question":"Le PGCD de 12 et 18 est :","option_a":"2","option_b":"3","option_c":"6","option_d":"12","option_e":"","option_f":"","bonne_reponse":"C","explication":"Les diviseurs de 12 sont {1, 2, 3, 4, 6, 12} et ceux de 18 sont {1, 2, 3, 6, 9, 18}. Le plus grand commun diviseur est 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":5757,"question":"Vrai ou Faux ? Deux nombres premiers entre eux ont toujours un PGCD égal à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, deux nombres sont premiers entre eux si leur PGCD est égal à 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":5758,"question":"Quel théorème permet d'affirmer que si a divise bc et si a est premier avec b, alors a divise c ?","option_a":"Théorème de Pythagore","option_b":"Théorème de Gauss","option_c":"Théorème de Bézout","option_d":"Théorème de Thalès","option_e":"","option_f":"","bonne_reponse":"B","explication":"Le théorème de Gauss stipule que si a divise bc et si a est premier avec b, alors a divise c.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":5759,"question":"La division euclidienne de 47 par 5 donne un quotient de 9 et un reste de :","option_a":"2","option_b":"3","option_c":"4","option_d":"5","option_e":"","option_f":"","bonne_reponse":"A","explication":"47 = 5 × 9 + 2. Le reste est donc 2, car 0 ≤ 2 \u003C 5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":5760,"question":"Vrai ou Faux ? Si a ≡ b [n], alors n divise (a - b).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Par définition, a ≡ b [n] signifie que n divise (a - b).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":5761,"question":"Quel est le PPCM de 4 et 6 ?","option_a":"12","option_b":"24","option_c":"8","option_d":"10","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les multiples de 4 sont {4, 8, 12, 16, 20, 24, ...} et ceux de 6 sont {6, 12, 18, 24, ...}. Le plus petit commun multiple est 12.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":5762,"question":"Vrai ou Faux ? Si a et b sont deux entiers non nuls, alors PGCD(a,b) × PPCM(a,b) = |a × b|.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Cette propriété est vraie et permet de calculer le PPCM à partir du PGCD et inversement.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":5763,"question":"Quel est le reste de la division euclidienne de -17 par 4 ?","option_a":"-1","option_b":"1","option_c":"3","option_d":"4","option_e":"","option_f":"","bonne_reponse":"C","explication":"-17 = 4 × (-5) + 3. Le reste est 3, car 0 ≤ 3 \u003C 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":5764,"question":"Si a et b sont deux entiers tels que a = 5k + 3 et b = 5k' + 3 (k, k' ∈ ℤ), alors :","option_a":"a + b ≡ 1 [5]","option_b":"a × b ≡ 4 [5]","option_c":"a - b ≡ 0 [5]","option_d":"a² ≡ 2 [5]","option_e":"","option_f":"","bonne_reponse":"C","explication":"a - b = 5(k - k') ≡ 0 [5]. Les autres propositions ne sont pas toujours vraies.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]