Going through the quant strategy again but couldn’t quite figure out why they are equal. I understand the (x-1)x(x+1) bit but couldn’t quite understand the third point. We can decompose the 6 into 2 x 3 and then 8 into a 2^8 but how do we then reach the conclusion that their remainders are equal? I came across similar questions before but still couldn’t properly solve it.

But 8 \neq 2^8?

Apologies, I meant to say decompose 8 into 2^3. I can solve this question by choosing the numbers but I can’t grasp the intuition using math foundation.

Think of it like this. If you have the product of three even numbers, show that the number must be divisible by 8. It’s the same idea in this problem.