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Turkish Journal of Mathematics

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.

First Page

1248

Last Page

1259

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Mathematics Commons

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