In 2008 or earlier, Michel Mendès France asked for an instance of a real number x such that both x and 1/x are simply normal to a given integer base b. We give a positive answer to this question by constructing a number x such that both x and its reciprocal 1/x are continued fraction normal as well as normal to all integer bases greater than or equal to 2. Moreover, x and 1/x are computable, the first n digits of their continued fraction expansion can be obtained in O(n4) mathematical operations.Fil: Becher, Veronica Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; ArgentinaFil: Madritsch, Manfred G.. Centre National de la Recherche Scientifique; Francia