A characterization of nonprime powers

Authors

RAUL DURAN DIAZ
LUIS HERNANDEZ ENCINAS
AGUSTIN MARTIN MUÑOZ
JAIME MUÑOZ MASQUE
SEOK-ZUN SONG

Abstract

A criterion is presented in order to decide whether agiven integer is a prime power or not. The criterion associatesto each positive integer $m$ a finite set of integers$\mathcal{S}(m)$, each of them $\le m $ and the propertiesof this set are studied. The notion of complementary pairsin $\mathcal{S}(m)$ is introduced and it is proved that if one isable to determine a complementary pair $n,n^\prime $, thena partial factorization of the odd integer $m$ can be obtainedin polynomial time. Some particular cases and examples of these resultsare given.

DOI

10.3906/mat-1603-143

Keywords

Complementary pair, partial factorization, prime power

First Page

1248

Last Page

1259

Recommended Citation

DIAZ, RAUL DURAN; ENCINAS, LUIS HERNANDEZ; MUÑOZ, AGUSTIN MARTIN; MASQUE, JAIME MUÑOZ; and SONG, SEOK-ZUN (2017) "A characterization of nonprime powers," Turkish Journal of Mathematics: Vol. 41: No. 5, Article 15. https://doi.org/10.3906/mat-1603-143
Available at: https://journals.tubitak.gov.tr/math/vol41/iss5/15