Abstract

Indefinite equation is an unsolved problem in number theory. Through explo-ration, the author has been able to use a simple elementary algebraic method to solve the solutions of all three variable indefinite equations. In this paper, we will introduce and prove the solutions of Pythagorean equation, Fermat’s the-orem, Bill equation and so on.

Highlights

  • Indefinite equation is an unsolved problem in number theory

  • The author has been able to use a simple elementary algebraic method to solve the solutions of all three variable indefinite equations

  • We can use the number axis to verify that C is a positive integer. □

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Summary

Definition of Indefinite Equation

We know indefinite equation ( called Diophantine equation) that all unknowns and known numbers are positive integers [1] [2]. We will introduce their new solutions one by one

First Order Indefinite Equation Some Theorems
Fermat’s Last Theorem
Beal’s Conjecture Beal’s conjecture: if the indefinite equation
Conclusion
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