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...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.展开更多
基金Supported by NNSF(No. 19931020, No. 10001006 and No. 60273015)of China
文摘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.
