c-alculate-the-rest-of-the-division-of-2-n-by-3-n-N-

Question Number 120469 by mathocean1 last updated on 31/Oct/20

c a l c u l a t e t h e r e s t o f t h e d i v i s i o n o f

2^{n} b y 3; n \in N

Answered by mathmax by abdo last updated on 31/Oct/20

n = 2 k \Rightarrow 2^{n} = 2^{2 k} = 4^{k} we hsve 4 \approx 1 [3] \Rightarrow 4^{n} \approx 1 [3] \Rightarrow r = 1

n = 2 k + 1 \Rightarrow 2^{n} = 2^{2 k + 1} = 2 . 4^{k} we have 4^{k} \approx 1 [3] \Rightarrow 2 . 4^{k} \approx 2 [3] \Rightarrow

\Rightarrow r = 2