On the Littlewood conjecture in simultaneous Diophantine approximation
  For any given real number $\alpha$ with bounded partial quotients, we construct explicitly continuum many real numbers $\beta$ with bounded partial quotients for which the pair $(\alpha, \beta)$ satisfies a strong form of the Littlewood conjecture. Our proof is elementary and rests on the basic theory of continued fractions. 
Boris Adamczewski (ICJ), Yann Bugeaud (IRMA)