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A positive integer k is called a "lucky" number if the units digit of k^6 is 4. How many lucky numbers smaller than 1000 are there?

 Apr 6, 2021
 #1
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I think it is 1 because there is only one possible value which is 2.

 Apr 6, 2021
 #2
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$k^6\equiv 4\pmod{10}$ has solutions $k\equiv \pm 2\pmod{10}$.

 

So $2,8,12,18,22,28, ...$ all work.

 Apr 6, 2021

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