On certain sequences of integers
HTML articles powered by AMS MathViewer
- by K. Thanigasalam PDF
- Trans. Amer. Math. Soc. 200 (1974), 199-205 Request permission
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
- H. Davenport, On Waring’s problem for cubes, Acta Math. 71 (1939), 123–143. MR 26, DOI 10.1007/BF02547752
- K. Thanigasalam, On sums of positive integral powers, Bull. Calcutta Math. Soc. 62 (1970), 133–138. MR 280454
- K. Thanigasalam, A generalization of Waring’s problem for prime powers, Proc. London Math. Soc. (3) 16 (1966), 193–212. MR 205965, DOI 10.1112/plms/s3-16.1.193
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 200 (1974), 199-205
- MSC: Primary 10L10; Secondary 10J10
- DOI: https://doi.org/10.1090/S0002-9947-1974-0354605-6
- MathSciNet review: 0354605