对不定方程x^3+y^3+z^3=3的研究

Study of the Diophantine Equation x^3+y^3+z^3=3

不定方程x3+y3+z3=3的整数解问题是一个较古老且未得到完全解决的问题,在已找到的整数解中可发现,均有两个未知数的解相等。对于在两个未知数相等的情况下有无整数解进行一定的研究和推进,并且证明了x3+y3+z3=3的解存在的形式。

The integer solution to the equation x^3 ＋ y^3 ＋ z^3 = 3 is an old problem which, until now, cannot be resolved completely. Among the integer answers available, the answers to any two unknowns are equal; yet, in the case that the two unknowns are equal, is there integer answer？ This paper studies this problem, and brings forth the form of the answers.