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Inductive Rings and Systems of Diophantine Equations

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Abstract

In this paper, by using model-theoretic methods, it is shown that some systems of unsolved cubic diophantine equations in number theory can have solutions in certain inductive extension rings of the ring I of rational integers. These inductive rings are not fields, and every element of them is a sum of 4 cubes and a sum of 3 squares. Also some of them satisfy the Goldbach conjecture and some others don’t.

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Authors and Affiliations

  1. College of Information Science, Beijing Normal University, Beijing 100875, P. R. China

    Rong Fang Bie

  2. School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China

    Shi Qiang Wang

Authors
  1. Rong Fang Bie
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  2. Shi Qiang Wang
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Correspondence to Rong Fang Bie.

Additional information

Supported by NNSF (No. 19931020, No. 10001006 and No. 60273015) of China

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Bie, R.F., Wang, S.Q. Inductive Rings and Systems of Diophantine Equations. Acta Math Sinica 22, 1549–1556 (2006). https://doi.org/10.1007/s10114-005-0834-8

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  • DOI: https://doi.org/10.1007/s10114-005-0834-8

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