Are all RR Lyrae stars modulated?

We analyzed 151 variables previously classified as fundamental mode RR Lyrae stars from Campaigns 01-04 of the Kepler two-wheel (K2) archive. By employing a method based on the application of systematics filtering with the aid of co-trending light curves in the presence of a large amplitude signal component, we searched for additional Fourier signals in the close neighborhood of the fundamental period. We found only 13 stars without such components, yielding the highest rate of modulated (Blazhko) stars detected so far (91 %). A detection efficiency test suggests that this occurrence rate likely implies a 100 % underlying rate. Furthermore, the same test performed on a subset of the Large Magellanic Cloud RR Lyrae stars from the MACHO archive shows that the conjecture of high true occurrence rate fits well to the low observed rate derived from this database.