Approximation simultanée dʼun nombre v-adique et de son carré par des nombres algébriques

We generalize to an arbitrary number field the result of Davenport and Schmidt about approximation to a real number and his square by rational numbers with the same denominator, as well as its p-adic analog due to Teulié. By an extension of Royʼs method, we prove that our new result is optimal.