I am looking for solutions for the diophantine equation
where $a\in \Bbb N$ and $b\in \Bbb N$.
Is there a power of $3$ that gives a power of $2$ when you add $1$?
Two solutions are easy to find:
- $3^0+1=2^1 \rightarrow 1+1=2$
- $3^1+1=2^2 \rightarrow 3+1=4$
But I'm looking for other solutions (solutions where $a>1$).
I believe that there is no other solution, but how can you proof this conjecture?
How can you find solutions for
where $p_1$ and $p_2$ are prime and $a,b,n\in \Bbb N$?