Prove that $10152^8-10887^8+27195^8$ is divisible by $26460$.

The very first thing that we need to do is to factorize $26460$ as [MATH]\color{yellow}\bbox[5px,purple]{26460=2^2\cdot 3^3\cdot 5\cdot 7^2}[/MATH]. The next thing we have to accomplish is to show that $10152^8-10887^8+27195^8$ is divisible by $2^2\cdot 3^3\cdot 5\cdot 7^2$, either

1. all at once or
2. separately.

But, I am sure you will also work out the prime factors for the other three numbers

$10152=2^3\cdot 3^3\cdot 47$; $10887=3\cdot 19\cdot 191$; $27195=3\cdot 5\cdot 7^2\cdot 37$