I can't find a way to prove that the following equation has only one solution :

X = (2^Q - 1) / (2^(P+Q) - 3^P)

with X,P,Q integers > 0

The trivial solution is X = 1, P = 1, Q = 1

Does anyone has an idea ? Best regards

I can't find a way to prove that the following equation has only one solution :

$$ X = \frac{2^Q - 1}{2^{P+Q} - 3^P} $$

with $X,P,Q$ integers $> 0$.

One trivial solution is $X = 1, P = 1, Q = 1$.

Does anyone has an idea ? Best regards