Answer by Servaes for Is $100$ the only square number of the form $a^b+b^a$?
(21-03-2020) Update: As no unconditional answer has yet been given, I will include a few more conditions that any solution must satisfy. The results used are rather advanced, so I will only include...
View ArticleAnswer by W-t-P for Is $100$ the only square number of the form $a^b+b^a$?
$\newcommand{\eps}{\varepsilon}$$\newcommand{\rad}{\mathrm{rad}}$At least, under the abc conjecture, there can be only finitely many pairs $(a,b)$with $b>a>1$ coprime such that $a^b+b^a$ is a...
View ArticleIs $100$ the only square number of the form $a^b+b^a$?
Conjecture$100$ is the only square number of the form $a^b+b^a$ for integers $b>a>1$.In other words, $(a,b)=(2,6)$ is the only solution. Can we prove/disprove this?ObservationsThe solution...
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