PMO 1

$16^{15}-8^{15}-4^{15}-2^{15}-1^{15}$ Can be written after factorising as

$16^{15}$ - [ $2^{15}+1$ ].[ $2^{30}+1$ ].. Eq1

Let $2^{15}+1$ be $a$

Let $2^{30}+1$ be $b$

$a$ is congruent to 33 mod 96

$b$ is congruent to 65 mod 96

$ab$ is congruent to 33 mod 96 .

And $16^{15}$ is congruent to 64 mod 96

So when Eq1 is checked mod 96 then 64-33= 31 is the answer.