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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Signed sums of polynomial values


Author: Hong Bing Yu
Journal: Proc. Amer. Math. Soc. 130 (2002), 1623-1627
MSC (2000): Primary 11A67, 11P05
Published electronically: November 15, 2001
MathSciNet review: 1887008
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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}


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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: http://dx.doi.org/10.1090/S0002-9939-01-06461-9
PII: S 0002-9939(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