Réponse:

en déduire les valeurs de n tel que n^3–n divise n+2 €N.

division euclidienne :

n+2

n³ – n |_____________________

-n³ – 2n² n² – 2n – 4 + 4 – 5

_______

–2n² –n

+2n² – 4n

________

–4n –n

+ 4n + 8

___________

8 – n

–8 – 4n

_________

–5n

+ 5n + 10

________

10

donc n³ - n = n² – 2n – 5 + (10/n+2)

n² – 2n – 5 = 0

delta= (-2)² – 4(1)(–5)

= 20 + 4 = 24

√ delta = 2√6

N1 = (2– 2√6)/2

= 1–√6