Comment on "NMR Experiment Factors Numbers with Gauss Sums"

Mehring et al. have recently described an elegant nuclear magnetic resonance (NMR) experiment implementing an algorithm to factor numbers based on the properties of Gauss sums. Similar experiments have also been described by Mahesh et al. In fact these algorithms do not factor numbers directly, but rather check whether a trial integer $\mathrm{\ell }$ is a factor of a given integer $N$. Here I show that these NMR schemes cannot be used for factor checking without first implicitly determining whether or not $\mathrm{\ell }$ is a factor of $N$.