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SquareFreeQ

SquareFreeQ[expr]
gives True if expr is a square-free polynomial or number, and False otherwise.
SquareFreeQ
gives True if expr is square free with respect to the variables vars.
MORE INFORMATION
  • For integers m and n, SquareFreeQ[m+I n] automatically works over the Gaussian integers.
  • The following options can be given:
GaussianIntegersAutomaticwhether to allow Gaussian integers
Modulus0modulus for polynomial coefficients
EXAMPLESCLOSE ALL
Basic Examples   (2)
12 has a factor 4, which is a square:
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12 has a factor 4, which is a square:
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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:
Properties & Relations   (3)
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:
Neat Examples   (2)
Square-free integers:
Square-free Gaussian integers:
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