Square-free number
This article defines a property that can be evaluated for natural numbers
Definition
A natural number is said to be square-free if there is no prime number for which divides .
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 |