Weaker generalization of the Catalan conjecture.

Question

The generalized Catalan conjecture states that for every natural number n, there are only finitely many pairs of perfect powers with difference n, i.e $x^a - y^b = n$ has finite solutions. What can be said about a weaker version, namely $x^a - y^b = x-y$. The only solutions I know are $3^2-2^3 = 3-2$ and $13^3-3^7 = 13 - 3$. Can it be shown that there are finite solutions for $(x,y)$ or if there are only a finite number of $(x,y)$