Waring's problem for Beatty sequences and a local to global principle
Banks, W. D.
Güloğlu, A. M.
Vaughan, R. C.
Journal de Theorie des Nombres de Bordeaux
Universite de Bordeaux I
1 - 16
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We investigate in various ways the representation of a large natural number N as a sum of s positive k-th powers of numbers from a fixed Beatty sequence. Inter alia, a very general form of the local to global principle is established in additive number theory. Although the proof is very short, it depends on a deep theorem of M. Kneser. © Société Arithmétique de Bordeaux, 2014, tous droits réservés.