If $n$  is a positive integer, then $2^{4n}-15n-1$  is divisible by

$p\left(1\right)=2^4-15-1=0$

True function $n=1$

Let us assume that $p\left(n\right)$  is true function $n=k$

Put $n=2$

$=2^{4\left(2\right)}-15\left(2\right)-1$

$=225$