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Etudes sur les équations de Ramanujan-Nagell et de Nagell-Ljunggren ou semblables
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Dans cette thèse, on étudie deux types d’équations diophantiennes. Une première partie de notre étude porte sur la résolution des équations dites de Ramanujan-Nagell Cx2+ b2mD = yn. Une deuxième partie porte sur les équations dites de Ngell-Ljunggren xp+ypx+y = pezq incluant le cas diagonal p = q. Les nouveaux réesultats obtenus seront appliqués aux équations de la forme xp + yp = Bzq. L’équation de Catalan-Fermat (cas B = 1) fera l’objet d’un traitement à part.
Title: Etudes sur les équations de Ramanujan-Nagell et de Nagell-Ljunggren ou semblables
Description:
Dans cette thèse, on étudie deux types d’équations diophantiennes.
Une première partie de notre étude porte sur la résolution des équations dites de Ramanujan-Nagell Cx2+ b2mD = yn.
Une deuxième partie porte sur les équations dites de Ngell-Ljunggren xp+ypx+y = pezq incluant le cas diagonal p = q.
Les nouveaux réesultats obtenus seront appliqués aux équations de la forme xp + yp = Bzq.
L’équation de Catalan-Fermat (cas B = 1) fera l’objet d’un traitement à part.
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