Express through basic quantifiers on the given domain:

[albert1992]

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.

 

[HallsofIvy]

What's wrong with the obvious, "For all y in Z, y² does not divide x"?

 

[albert1992]

I think it works but what about 1

1 squared does divide the square free 1