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   How Many Integers
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   Author  Topic: How Many Integers  (Read 567 times)
navdeep1771
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How Many Integers  
« on: Apr 12th, 2019, 9:25am »
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How many integers from 1 to 10^6 (both inclusive) are neither perfect squares nor perfect cubes nor perfect fourth powers?
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rmsgrey
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Re: How Many Integers  
« Reply #1 on: Apr 12th, 2019, 9:59am »
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Answer: 998910
 
Reasoning:
 
hidden:

1000000=10002=1003=106
1=12=13=16
 
So there are 1000 squares, 100 cubes, and 10 sixth powers (which are both squares and cubes). All fourth powers are also squares, so can be ignored.
 
So there are 1000+100-10 = 1090 numbers which are squares or cubes (or both) in the range and 1000000-1090 numbers which are neither.
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