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How many different rational numbers between 1/1000 and 1000 can be written either as a power of 2 or as a power of 3 or as a power of 5, where the exponent is a (possibly negative) integer?

 Jan 2, 2021
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Powers of 2 =(-9, -8,  -7, -6, -5, -4, -3, -2,  -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9)=19

 

Powers of 3=(-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6)=13

 

Power of 5=(-4, -3, -2, -1, 0, 1, 2, 3, 4)=9


Powers of [2, 3, 5]=19 + 13 + 9 =41 rational numbers can be written as powers of 2 or 3 or 5.

 Jan 2, 2021

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