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Related Experiment Video

Updated: Jan 28, 2026

A Generalized Method for Determining Free Soluble Phenolic Acid Composition and Antioxidant Capacity of Cereals and Legumes
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On and some of its generalizations.

Tingting Bai1

  • 1College of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji, China.

Journal of Inequalities and Applications
|March 7, 2019
PubMed
Summary

This study presents a simple method to solve the Diophantine equation x^n + y^n = z^2. It proves that this equation has a limited number of positive integer solutions for any positive integers m and n.

Area of Science:

  • Number Theory
  • Algebraic Geometry

Background:

  • Diophantine equations are polynomial equations with integer solutions.
  • The specific equation x^n + y^n = z^2 is a variation of Fermat's Last Theorem.

Purpose of the Study:

  • To develop a straightforward method for solving the Diophantine equation x^n + y^n = z^2.
  • To determine the finiteness of positive integer solutions for this equation.

Main Methods:

  • The study employs elementary number theoretic techniques.
  • A direct approach is used to derive the solutions.

Main Results:

  • A simple method for solving the Diophantine equation x^n + y^n = z^2 is presented.
  • It is proven that for any positive integers m and n, the equation has a finite number of positive integer solutions for x, y, and z.
Keywords:
Diophantine equationInteger solution

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Conclusions:

  • The findings offer a clear pathway to solving a specific class of Diophantine equations.
  • The established finiteness of solutions contributes to the understanding of Diophantine equation properties.