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In this paper we consider $N$, the number of solutions $(x,y,u,v)$ to theequation $ (-1)^u r a^x + (-1)^v s b^y = c$ in nonnegative integers $x, y$ andintegers $u, v \in \{0,1\}$, for given integers $a>1$, $b>1$, $c>0$, $r>0$ and$s>0$. We show that $N \le 2$ when $\gcd(ra, sb) =1$ and $\min(x,y)>0$, exceptfor a finite number of cases that can be found in a finite number of steps. Forarbitrary $\gcd(ra, sb)$ and $\min(x,y) \ge 0$, we show that when $(u,v) =(0,1)$ we have $N \le 3$, with an infinite number of cases for which N=3.

The generalized Pillai equation $\pm r a^x \pm s b^y = c$