Question

Aratati ca ( 2 la n-2+2la n ) |(4la n+1+4 la n) n€N
Va rog ajutatima!!!!

Answer 1

$a=2^{n-2}+2^n=2^{n-2}(1+4)=5\cdot 2^{n-2}$

$b=4^{n+1}+4^n=4^n(4+1)=5\cdot 4^n=5\cdot 2^{2n}=5\cdot 2^{n-2}\cdot 2^{n+2}=2^_n+2}\cdot a$

Deci $a|b$