(In reply to
re: Solution by Steve Herman)
A piece of math trivia is that 8 and 9 are the only consecutive perfect powers. More formally this is written in the form of Catalan's Conjecture:
The equation x*a - y^b = 1 with x,y>0 and a,b>1
has exactly one solution for which all a,b,x,y are integers.
That solution is 3^2 - 2^3 = 1
A proof of the conjecture was accepted around 2003-4. More specifically the subcase where the bases are limited 2 and 3 was proven before Catalan formally published his conjecture.
https://en.wikipedia.org/wiki/Catalan's_conjecture
https://mathworld.wolfram.com/CatalansConjecture.html
I probably should have included information this in my solution, or if I was feeling ambitious proven the bases 2 and 3 subcase.
re(2): Solution
