Question

FIE a ∈ R, a diferit de 0. Folosind metoda inductiei matematice complete, aratati ca daca a + 1/a ∈ Z , atunci a ^n + 1/ a ^n ∈ Z , ∀ n ∈ Z .

Answer 1

pai, presupui a^n+1/a^n apartine Z, => a^(n+1)+a/a^(n+1)=a(a^n+1)/a*a^n=a^n+1/a^n care e Adevarat ;)