all the powers of 4 in the range 4 through 1000
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we can check
4^1=4
4^2=16
4^3=64
4^4=128
4^5=1028
we can clearly see that
in the range of 4 and 1000 the number that exists are
(1,2,3,4)
4^1
4^2
4^3
4^4
exists in this range
this is an easy way to solve this problem
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