TITLE:
Multiway Generalization of Euler Proposition
AUTHORS:
Zhongqi Zhou
KEYWORDS:
Indefinite Equation, Generalization of Euler Proposition, Induction, Positive Integer Solution, Conjecture
JOURNAL NAME:
Open Access Library Journal,
Vol.12 No.2,
February
26,
2025
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.