Given the linear diophantine $3^n x - 2^n y = 1$, ($n$ being a natural parameter) it's well known that it has infinitely many solutions.
My question is whether we can find a generic particular solution of it in terms of $n$.
I inspected some values using the online linear diophantine solver > https://www.math.uwaterloo.ca/~snburris/htdocs/linear.html yet found no pattern.
I also tried to conjecture the inverse of $3^n$ modulo $2^n$ in terms of $n$ assuming a formula could be found but in vain.
Any ideas are welcome. Thanks.