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?

Guest Jun 29, 2021

#1**0 **

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.

=^._.^=

catmg Jun 30, 2021