For complex number $z$ and $w$, if $|z|^2 - w - |w|^2 = z - w$ then
Step-by-Step Solution
Key Concept: A product of consecutive integers contains all prime factors required for divisibility by factorials.
The product $P = (n-10)(n-9)(n-8)\cdots(n-10)$ of 21 consecutive integers is divisible by $21!$. This product can be shown to be divisible by $2! \cdot 3! \cdot 4! \cdot 5! \cdot 6!$ because it contains enough factors to form these factorials. The divisibility follows from the fact that consecutive integer products contain all necessary prime factors.
Correct Answer: 1,2