Proof By Induction Help (1 Viewer)

[mathscrazy24]

Hi, looking for help with this divisibility question:
Prove by induction that (3^(2n)^2) - 1 is divisible by 8

 

[liamkk112]

to make your life simpler, prove 3^(2n) -1 is always divisible by 8, for n>=1. then you’ve also proven your question, since if it holds for any even natural number then it holds for (2n)^2 since that’s an even natural number
as a sketch
base case:n=1 gives 9-1=8
assume 3^(2k)-1 =8r for some integer r
then 3^2(k+1)-1
=9•3^(2k)-1
= 9•(8r+1)-1
= 8(9r+1)
as required