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Transactions of the American Mathematical Society
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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1974-0354605-6
PII: S 0002-9947(1974)0354605-6
Article copyright: © Copyright 1974 American Mathematical Society