is the prime factorization of into distinct primes, then is always false for square-free .
Note: we assume here that itself must be greater than 1; hence 1 is not considered square-free. However, one must be alert to the particular context in which “square-free” is used as to whether this is considered the case.
The name derives from the fact that if any were to be greater than or equal to two, we could be sure that at least one square divides (namely, .)
1 Asymptotic Analysis
- 1 R. C. Baker and J. Pintz. The distribution of square-free numbers. Acta Arith., 46:73–79, 1985. http://www.emis.de/cgi-bin/zmen/ZMATH/en/quick.html?type=html&an=0535.10045Zbl 0535.10045.
|Date of creation||2013-03-22 11:55:33|
|Last modified on||2013-03-22 11:55:33|
|Last modified by||akrowne (2)|
|Synonym||square free number|