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?
+1622 k^6 = something that ends in 4.
Notice that something that ends in 4 has to be e^6 where e is even. 6 wont work because 6^n always ends in 6.
2^6 = 64 that works
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 6
4^6 = 2^12 = 6 so 4 doesnt work
8^6 = 2^18 = 2^[(4*4) + 2] = 4.
So only 2 and 8 work. 12 and 18 also work. 2, 12, 22, 32... 992. 8, 18, 28... 998.
Each of those sets have 100 elements. So there are 200 lucky numbers.
