Prove by mathematical induction that 3^2^n is divisible by 8 for all positive integers n.?

Question

I have seen how others have explained it on the internet, but I have no idea where the numbers come from. And this double exponent thing is killing me, please help!!

Answer 1

It isn't. Unless there is a typo 3^2^n is never divisible by 8.

Depending on if you're doing 3²^n or 3^(2^n). 3²^n would be 3^(2n).

Either way knowing this the prime factorization of either statement would be 3 to the 2nth power or the 2^nth power. Either way 3 to any integer power clearly is never equal to 8, and thus is never equal to any multiple of 8.