This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# SquareFreeQ

 SquareFreeQ[expr] gives True if expr is a square-free polynomial or number, and False otherwise. SquareFreeQgives True if expr is square free with respect to the variables vars.
• For integers m and n, SquareFreeQ[m+I n] automatically works over the Gaussian integers.
• The following options can be given:
 GaussianIntegers Automatic whether to allow Gaussian integers Modulus 0 modulus for polynomial coefficients
12 has a factor 4, which is a square:
 Out[1]=
12 has a factor 4, which is a square:
 Out[2]=

 Out[1]=
 Out[2]=
 Scope   (6)
Integers:
Gaussian integers:
Univariate polynomials:
Multivariate polynomials:
Polynomials in specific variables:
Polynomials over a finite field:
This is square free over the integers:
 Options   (2)
Square-free Gaussian integers:
Square-free polynomials over finite fields:
 Applications   (1)
The central binomial coefficients Binomial are not square free for n>4:
Square factors can be found using FactorSquareFreeList:
The polynomial p[x]/PolynomialGCD[p[x], p'[x]] is always square free:
MoebiusMu is zero for non-square-free integers:
Square-free integers:
Square-free Gaussian integers:
New in 6