Turkish Journal of Mathematics
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, R. D, ENCINAS, L. H, MUÑOZ, A. M, MASQUE, J. M, & SONG, S (2017). A characterization of nonprime powers. Turkish Journal of Mathematics 41 (5): 1248-1259. https://doi.org/10.3906/mat-1603-143
