Question

Ex 9 va rog ajutati-mă!

Answer 1

$a = 72^{n+1} - 2^{3n}\cdot 3^{2n}\\\\ a = 72^{n+1} - {(2^3)}^n\cdot {(3^2)}^n\\\\a = 72^{n+1} - {(8\cdot 9)}^n\\\\ a = 72^{n+1} - 72^n\\\\ a = 72^n(72 - 1)\\\\ a = 72^n\cdot 71\\\\ \implies a \in M_{71} \implies 71 \mid a, \forall n \in \mathbb{N}$