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On Fabry's gap theorem

Jan-Christoph Puchta (2002)

Archivum Mathematicum

By combining Turán’s proof of Fabry’s gap theorem with a gap theorem of P. Szüsz we obtain a gap theorem which is more general then both these theorems.

On Gelfond’s conjecture about the sum of digits of prime numbers

Joël Rivat (2009)

Journal de Théorie des Nombres de Bordeaux

The goal of this paper is to outline the proof of a conjecture of Gelfond [6] (1968) in a recent work in collaboration with Christian Mauduit [11] concerning the sum of digits of prime numbers, reflecting the lecture given in Edinburgh at the Journées Arithmétiques 2007.

On generalized square-full numbers in an arithmetic progression

Angkana Sripayap, Pattira Ruengsinsub, Teerapat Srichan (2022)

Czechoslovak Mathematical Journal

Let a and b . Denote by R a , b the set of all integers n > 1 whose canonical prime representation n = p 1 α 1 p 2 α 2 p r α r has all exponents α i ( 1 i r ) ...

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