Seems a bit of a troll problem, I think? We claim that no $3 \pmod 8$ numbers can be represented in this form. Indeed, if $a$ is even and $b$ is odd, then $a^{bc}-b^{ad} \equiv 0-1 \equiv 7 \pmod 8$, while if $a$ is odd and $b$ is even, then $a^{bc}-b^{ad} \equiv 1 -0 \equiv 1 \pmod 8$, and so we may conclude.