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# lucky numbers

+1
107
2

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
-1

I think it is 1 because there is only one possible value which is 2.

Apr 6, 2021
#2
+602
+1

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

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

Apr 6, 2021