Express through basic quantifiers on the given domain:

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Homework Statement


x is square free (not divisible by a perfect square) on Z


Homework Equations


Z meaning all integers.


The Attempt at a Solution


I did a similar problem earlier that asked for the expression for prime numbers on the Natural numbers domain. For that problem the product of a*b with a,b >1 never equaled a prime number. So for this problem I believe that all of the prime numbers are included in the square free I'm just not sure how to integrate this.
 
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What's wrong with the obvious, "For all y in Z, y2 does not divide x"?
 
I think it works but what about 1

1 squared does divide the square free 1
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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