Inspired by Problem 4, IMO 2006
Number Theory
Level
4
\[\large p^{3a+1}+p^a+1=b^p\]
Find all solutions to the Diophantine equation above, where \(a\) and \(b\) are positive integers and \(p\) is an odd prime, and enter your answer as \(\sum (a+b+p)\).
by
Kazem Sepehrinia