User blog comment:QuasarBooster/Potentially googological function from number theory?/@comment-35470197-20181220232542

Generally, a number theoretic equation, e.g. Fermat's last theorem and abc conjecture, is very hard to understand whether it has a solution or not. So if there is no obvious way to find an upperbound, it is very hard to verify the existence of a solution. Also, I have no idea about how large the solution is if we assume that it exists. Interesting.