For all a>0 , what is the remainder when a^400 is divided by a^3+1. Can you please refer to the concepts required to understand this. I am not understanding the solution

a^400 + a^397 = a^397(a^3 + 1), which is divisible by a^3 + 1
-a^397 -a^394 = -a^394(a^3 + 1), which is divisible by a^3 + 1
... -a^7 - a^4 = -a^4(a^3 + 1) is divisible by a^3 + 1

Adding all the terms,

a^400 + a^397 - a^397 - a^394 + a^394 + a^391 - a^391 - ....- a^4 = k*(a^3 + 1)

=> a^400 - a^4 = k(a^3 + 1)

=> a^400 - a^4 leaves a remainder 0 when divided by a^3 + 1
So, the remainder when a^400 is divided by a^3+1 is the same as the remainder when a^4 is divided by a^3+1

a^4 mod a^3 + 1 = a^3 - a + 1