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Multiway Generalization of Euler Proposition

DOI: 10.4236/oalib.1112789, PP. 1-15

Keywords: Indefinite Equation, Generalization of Euler Proposition, Induction, Positive Integer Solution, Conjecture

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Abstract:

In this paper, the multiway extension of the Euler proposition is presented. By means of inductive reasoning, it is proved that there are positive integer solutions to five kind of indefinite equations, and the uniqueness of the solution of the indefinite equations in these propositions is demonstrated. Three related conjectures are proposed. Finally, the general method to understand these indeterminate equations is pointed out. 

References

[1]  T. 库安格. 一个欧拉命题的简单证明[J]. 数学通讯, 1992(8): 34.
[2]  柯召, 孙琦. 谈谈不定方程[M]. 哈尔滨: 哈尔滨工业大学出版社, 2011: 15.
[3]  Zhou, Z.Q. (2024) The Solution of the Indefinite Equation by the Method ean Algorithm. Open Access Library Journal, 11, e12011. https://doi.org/10.4236/oalib.1112011

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