Question

demonstrati ca (n+3)(n+5)(n+7)⋮3 ∀ n∈N

Answer 1

Salut , ai de analizat 3 cazuri:

i) n=3k : (3k+3)(3k+5)(3k+7)= 3(k+1)(3k+5)(3k+7) ⋮ 3

ii)n=3k+1: (3k+4)(3k+6)(3k+8)=3(3k+4)(k+2)(3k+8) ⋮ 3

iii)n=3k+2: (3k+5)(3k+7)(3k+9)= 3(3k+5)(3k+7)(k+3) ⋮ 3

Sper ca te-am ajutat. O zi buna!