Question

Fie E(n)=2n^3+3n^2+3n+1 napartine N*
De aratat ca E(n) are ca divizor un numar impar diferit de 1

Answer 1

E(n) =2n²(n+1) + n(n+1) + 2n+1 = n(n+1)(2n+1) + (2n+1) = (2n+1)(n²+n+1)
⇒ (2n+1) | E(n)    2n + 1 = nr. impar  ⇒ daca n ∈ N*  2n+1 ≠1