Find all positive integers k and l such that 3^{k} - 2^{l} = 1

This is the last part of a question and I have previously proved that 2^{l} + 1 is divisible by 27 iff it is also divisible by 19 and did this by examining the sequence of powers of 2 reduced modulo 27 and the sequence of powers of 2 reduced modulo 19.

I'm assuming this somehow relates to this proof but not sure how to start?