  We consider $N$, the number of solutions $(x,y,u,v)$ to the equation $ (-1)^u
r a^x + (-1)^v s b^y = c $ in nonnegative integers $x, y$ and integers $u, v
\in \{0,1\}$, for given integers $a>1$, $b>1$, $c>0$, $r>0$ and $s>0$. Previous
work showed that there are nine essentially distinct $(a,b,c,r,s)$ for which $N
\ge 4$, except possibly for cases in which the solutions have $r$, $a$, $x$,
$s$, $b$, and $y$ each bounded by $8 \cdot 10^{14}$ or $2 \cdot 10^{15}$. In
this paper we show that there are no further cases with $N \ge 4$ within these
bounds. We note that $N = 3$ for an infinite number of $(a,b,c,r,s)$, even if
we eliminate from consideration cases which are directly derived from other
cases in one of several completely designated ways. Our work differs from
previous work in that we allow $x$ and $y$ to be zero and also allow choices of
$(u,v)$ other than $(0,1)$.
