Improvement of an estimate of H. Müller involving the order of 2(mod u)

Abstract.

For u odd the order $\ell (u)$ of 2(mod u) in $({\Bbb Z}/u {\Bbb Z})^*$ exists. Recently Helmut Müller has given an estimate for $\sum\limits _{u\le x\atop q\nmid \ell (u)}1$ in this journal, with q an odd prime. This estimate is sharpened.