Séminaire de Théorie Analytique des Nombres et Problèmes Diophantiens

Le 14 juin 2001

Natarajan Saradha (Tata Institute of Fundamental Research)

Some extensions and refinements of a theorem of Sylvester.

 Résumé : An old result of Sylvester says that the greatest prime factor of the product $n(n+d)\cdots (n+(k-1)d)$ exceeds k provided $n \geq d+k.$Here n,d,k denote positive integers with gcd(n,d)=1. In this talk we give some improvements of this result obtained recently and its application to the problem of perfect powers in arithmetic progression.

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