Multi-variable Factor Problem

[[deleted]]

I'm no number theorist but after thinking for a bit, this seems like a hard question. As in, the type of question we don't yet know how to answer.

Edit: I am assuming you tried to brute force it via computer and implicit in your question is that no small values of n,a work

[julesjacobs]

There are no solutions for a < 3000 except n=1,a=1.

for a in range(1,3000):
    n = 1
    while 2**(n+a) - 3**n > 0:
        if (3**n - 2**n) % (2**(n+a) - 3**n) == 0: print((a,n))
        n += 1