bump bump

if $n$ is of the form $7^k-3^k$ where $k$ divides $n-1$ then , indeed $n$ divides $7^{n-1}-3^{n-1}$ Suppose $k=3^l$........Then $n=7^{3^l}-3^{3^l}$ Also , $n$ is composite as $7^{3^l}-3^{3^l} \equiv (-1)^{3^l}-3^{3^l} \equiv 4$ mod $8$ However by LTE : $u_{3}(7^k-1)=u_{3}(7-1)+u_{3}(k)=l+1$ So, $k=3^l|7^{3^l}-1$, thus it also divides $n-1=7^{3^l}-3^{3^l}-1$ since there are infinetely many such $k$, we are done