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On Waring's Problem with Cubic Polynomial Summands


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1 National Tsing Hua University, China
     

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Let a cubic integral-valued polynomial be represented by

P(x) = 1/6a(x3-x)+1/6b(x2-x)+cx+d,

where a, b, c and d are integers with (a, b, c) = 1 and a > 0. The object of this paper is to prove that the Diophantine equation

P(x1) + ...+P(x<sub8)=N xn>0

is soluble for all sufficiently large integers N. This result is better than my previous one, where we require nine values of P(x), x ≥ 0.


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  • On Waring's Problem with Cubic Polynomial Summands

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Authors

Hua Loo Keng
National Tsing Hua University, China

Abstract


Let a cubic integral-valued polynomial be represented by

P(x) = 1/6a(x3-x)+1/6b(x2-x)+cx+d,

where a, b, c and d are integers with (a, b, c) = 1 and a > 0. The object of this paper is to prove that the Diophantine equation

P(x1) + ...+P(x<sub8)=N xn>0

is soluble for all sufficiently large integers N. This result is better than my previous one, where we require nine values of P(x), x ≥ 0.