Question

For what least value of $n$, $(2^{6n}-6^{2n})$ is divisible by $n$, being even +ve.

Answer 1

$2^{6n}-6^{2n}={\left(2^6\right)}^n-\left(6^2\right)n^n={64}^n-{36}^n$
Clearly it is divisible by 64+36=100