Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On certain sequences of integers


Author: K. Thanigasalam
Journal: Trans. Amer. Math. Soc. 200 (1974), 199-205
MSC: Primary 10L10; Secondary 10J10
MathSciNet review: 0354605
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Abstract: Let the sequence $ \{ {k_i}\} $ satisfy $ 2 \leqslant {k_1} \leqslant {k_2} \leqslant \cdots $. Then, under certain conditions satisfied by $ \{ {k_i}\} $, it is shown that there exists an integer $ s$ such that the sequence of integers of the form $ x_1^{{k_1}} + \cdots + x_s^{{k_s}}$ has positive density. Also, some special sequences having positive densities are constructed.


References [Enhancements On Off] (What's this?)

  • [1] H. Davenport, On Waring's problem for cubes, Acta Math. 71 (1939), 123-143. MR 1, 5. MR 0000026 (1:5c)
  • [2] K. Thanigasalam, On sums of positive integral powers, Bull. Calcutta Math. Soc. 62 (1970), 133-138. MR 43 #6174. MR 0280454 (43:6174)
  • [3] -, A generalization of Waring's problem for prime powers, Proc. London Math. Soc. (3) 16 (1966), 193-212. MR 34 #5790. MR 0205965 (34:5790)

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DOI: http://dx.doi.org/10.1090/S0002-9947-1974-0354605-6
Article copyright: © Copyright 1974 American Mathematical Society