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 th powers. Let be an integral-valued polynomial of degree satisfying the necessary condition that there exists no integer dividing the values for all integers . Then, for every positive integer and every integer , there are infinitely many integers and choices of such that

**1.**M. N. Bleicher, On Prielipp's problem on signed sums of 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