i think it can also be attributed to people joining to gain access to the resources on bos (esp new hsc students who're scouring the internet for all the resources they can find)
ik a lot of people that just sign up for the resources on bos lol
careful the 2 isn't squared just do it again and u shud end up with 8M\times3^{4k+2}+3^{4k+2}-1 in step 3 (prove for n=k+1) at which point u just prove 3^{4k+2}-1 is divisible by 8 (i did it via mathematical induction)
just did it pretty simple
idk what ur having a problem with tho but make sure u prove the stuff that doesn't get multiplied by 8 is divisible by 8 the 3^{4k+2}-1 stuff