What is remainder when $5^6 - 3^6$ is divided by $2^3$ (method) I want to know the method through which I can determine the answers of questions like above mentioned one.
PS : The numbers are just for example. There may be the same question for BIG numbers.
Thnx.

Another method is to simply reduce mod $8$. We know that $5^2 = 25 \equiv 1 \bmod 8$ and $3^2 = 9 \equiv 1 \bmod 8$.
Thus:
$5^6 - 3^6 = (5^2)^3 - (3^2)^3 \equiv 1^3 - 1^3 \equiv 0 \bmod 8$.
So $8$ divides $5^6 - 3^6$ with no remainder.
