Mann Daniels
03/21/2023 · High School

Exercice2: 1) soit \( n \in \mathbb{N} \); montrer que ; \( n^{2}+3 n+3 \) est impair 2) \( 7^{2018}-1 \) est -il un nombre premier ? justifier la réponse 3) on pose: \( A=3^{n+3} \times 5^{n+1}-9 \) et \( n \in I N \) a) montrer que : \( A=9\left(15^{n+1}-1\right) \) b) quelle la parité de \( 15^{n+1} \) c) en déduire que: A est un multiple de 18 4) soit \( n \) un entier naturel tel que \( n>3 \) et on pose : \( X=\frac{2 n+7}{n-3} \)

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1) \( n^{2}+3n+3 \) est impair pour tout \( n \in \mathbb{N} \). 2) \( 7^{2018} - 1 \) n'est pas un nombre premier. 3) a) \( A = 9(15^{n+1} - 1) \). b) \( 15^{n+1} \) est impair. c) \( A \) est un multiple de 18. 4) \( X \) est un nombre réel positif et supérieur à 2.

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