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Signed sums of polynomial values


Author: Hong Bing Yu
Journal: Proc. Amer. Math. Soc. 130 (2002), 1623-1627
MSC (2000): Primary 11A67, 11P05
DOI: https://doi.org/10.1090/S0002-9939-01-06461-9
Published electronically: November 15, 2001
MathSciNet review: 1887008
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Abstract | References | Similar Articles | Additional Information

Abstract: We give a generalization of Bleicher's result on signed sums of $k$th powers. Let $f(x)$ be an integral-valued polynomial of degree $k$satisfying the necessary condition that there exists no integer $d>1$ dividing the values $f(x)$ for all integers $x$. Then, for every positive integer $n$and every integer $l$, there are infinitely many integers $m\ge l$ and choices of $\varepsilon _{i}=\pm 1$ such that

\begin{displaymath}n=\sum_{i=l}^{m}\varepsilon_{i}f(i).\end{displaymath}


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

  • 1. M. N. Bleicher, On Prielipp's problem on signed sums of $k$th powers, J. Number Theorey. 56(1996), 36-51. MR 96j:11011
  • 2. R. L. Graham, Complete sequences of polynomial values, Duke Math.J, 31(1964), 275-285. MR 29:63
  • 3. L. K. Hua, An easier Waring-Kamke problem, J. London Math. Soc. 11(1936), 4-5.
  • 4. D. E. Knuth and José Heber Nieto, Solution to Problem E3303, Amer. Math. Monthly. 97(1990), 348-349.
  • 5. M. B. Nathanson, ``Elementary Methods in Number Theory", volume 195 of Graduate Texts in Mathematics, Springer-Verlag, 2000. MR 2001j:11001

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Additional Information

Hong Bing Yu
Affiliation: Department of Mathematics, University of Science and Technology of China, Hefei 230026, Anhui, People’s Republic of China
Email: yuhb@ustc.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-01-06461-9
Received by editor(s): January 10, 2001
Published electronically: November 15, 2001
Additional Notes: The author was supported by the National Natural Science Foundation of China
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2001 American Mathematical Society

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