TITLE: Equation $x^2=y^p + 1$
QUESTION [11 upvotes]: can you help me please for solving this diophantine equation : $x^2=y^p+1$
and if you can give me a general method to studying such equation : $x^2=y^p+t$
Thanks

REPLY [2 votes]: For $t = 1$, your question is about a special case
of Catalan's conjecture, which has been proved in 2002
by Preda Mihăilescu.
In particular, for $t = 1$ the only solution is $3^2 = 2^3 + 1$.