Question

Plz ajutor.   Aratati ca 3^{45}+3^{44}+3^{43} se imparte exact la 13 

Answer 1

3⁴³(1+3+3²)=3⁴³ * (4+9)= 3⁴³ *13 :13= 3⁴³

Answer 2

Notam numarul $3^{45}+3^{44}+3^{43}$ cu  litera A
[tex] 3^{45}+3^{44}+3^{43}
Dam factor comun pe 3^{43}
3^{43}*( 3^{2}+3+1)=3^{43}*(9+3+1)=3^{43}*13 [/tex]
A=$13*3^{43}$⇒A divizibil cu 13