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Topic: How Many Integers (Read 567 times) 

navdeep1771
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How Many Integers
« on: Apr 12^{th}, 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 12^{th}, 2019, 9:59am » 
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Answer: 998910 Reasoning: hidden:  1000000=1000^{2}=100^{3}=10^{6} 1=1^{2}=1^{3}=1^{6} 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+10010 = 1090 numbers which are squares or cubes (or both) in the range and 10000001090 numbers which are neither. 


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