A characterization of nonprime powers

Authors

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

DOI

10.3906/mat-1603-143

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.

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