Suppose that \(\star(n) = \left\{n - 2, n + 2, 2n, \frac {n}{2}\right\} \). For example, \(\star(6) = \{3,4,8,12\} \). For how many distinct integers n does \(\star(n)\) have exactly three distinct elements?
There are three distinct integers n: 0, 2, 4.
There are 5 integers.
If you solve these 5 equations, you will get the 5 integers.
1) n - 2 = 2n
2) n - 2 = n/2
3) n + 2 = 2n
4) n + 2 = n/2
5) 2n = n/2
3)
