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An integer n is said to be square-free if the only perfect square that divides n is 1. How many positive odd integers greater than 1 and less than 1000  are square-free?

 Jun 29, 2021
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sqrt(1000) = 31.6227766017

So the number of squares from 1 to 1000 is 31. (1^2, 2^2, ..., 31^2)

Out of that list, 16 of them are odd squares. 

500 numbers from 1 to 1000 are odd. 

So 500 - 16 are odd numbers that aren't squares. 

 

=^._.^=

 

Edit:

Not square, but square free. 

Not sure how to do this question. 

I hope someone else can help more. 

Maybe casework, but 1000 is quite large.

 

=^._.^=

 Jun 30, 2021
edited by catmg  Jun 30, 2021

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