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An additive problem about powers of fixed integers

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Résumé

SoitA un ensemble fini d'entiers ≥2. Nous étudions les propriétés de l'ensemble Σ(Pow(A)) des entiers positifs qui sont une somme de puissances distinctes d'éléments deA. Erdõs posa le problème suivant: démontrer que Σ(Pow({3,4})) a densité asymtotique superieure positive. Nous démontrons que la fonction qui les énumère vérifieP {3,4}(x)≫x0.9659.

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References

  1. Burr S. A.—Erdõs P.—Graham R. L.—Wen-Ching Li W.,Complete sequences of sets of integer powers, Acta Arithmetica,77 (1996), 133–138.

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  2. Erdõs P.,personal communication, (1996) http://www.unil.ch/ima/docs/Personnes/gmelfi/erdos.html.

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  1. Institut de Mathématiques, Université de Lausanne, CH-1015, Lausanne, Switzerland

    Giuseppe Melfi

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  1. Giuseppe Melfi
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Melfi, G. An additive problem about powers of fixed integers. Rend. Circ. Mat. Palermo 50, 239–246 (2001). https://doi.org/10.1007/BF02844979

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  • DOI: https://doi.org/10.1007/BF02844979

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