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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?

 Jan 18, 2020
 #1
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There are three distinct integers n: 0, 2, 4.

 Jan 18, 2020
 #2
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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)  

 Jan 19, 2020

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