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Square-free number

This article defines a property that can be evaluated for natural numbers

Contents

Definition

A natural number n is said to be square-free if there is no prime number p for which p^2 divides n.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
cyclicity-forcing number every group of that order is cyclic see classification of cyclicity-forcing numbers |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
solvability-forcing number every group of that order is solvable square-free implies solvability-forcing any square of a prime is a counterexample |FULL LIST, MORE INFO