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We prove that there are only finitely many positive integers such that there is some integer such that is 1 or a prime for all , thus solving a problem of Byeon and Stark.
Nous obtenons une minoration d’une forme linéaire de logarithmes elliptiques de points algébriques d’une courbe elliptique à multiplication complexe définie sur . Cette minoration est optimale (à constante près) en la hauteur de la forme linéaire considérée.
We present a density result for the norm of the fundamental unit in a real quadratic order that follows from an equidistribution assumption for the infinite Frobenius elements in the class groups of these orders.
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