Question

prove by induction or any other prove methods

Answer 1

\[\huge{19|2^{2^{6n+2}}+3}\]

Answer 2

so far I let N be\[N=2^{6n+2}\]
\[19|2^N+3\]
\[n=0 \implies P(0)=2^4+3=19\]
\[P(k)=2^{2^{6k+8}}+3=2^{2^{6k+2}2^6}+3=(2^N)^{2^6}+3=(2N)^{64}+3\]

Answer 3

\[2^{63N}\color{blue}{(2^N+3)}-3 \times 2^{63N}+3\]
blue divisible by 19

Answer 4

now I need to show that \[19|-3 \times 2^{63N}+3=-3(2^{63N}-1)\]

Answer 5

sorry.... its ages since I've done induction...

Answer 6

lol idk im sorry i tried!

Answer 7

@mukushla

Answer 8

@phi @amistre64