I'm dealing with number theory now and I have an interesting question. Every number can be approximated with two perfect powers, where perfect power is a number in form $$a^b$$$$a,b \geq 2, a,b \in \mathbb N $$
My question is, how close can I approximate a given number? The number is huge.... So what can be smallest interval which contains the given number and its bounds are perfect powers?
Thank you!