Integral Solutions to Linear Indeterminate Equation

Changjiang Zhu

arXiv:1103.1418·math.AP·March 9, 2011·1 cites

Integral Solutions to Linear Indeterminate Equation

Changjiang Zhu

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TL;DR

This paper derives an explicit formula for all integral solutions to linear indeterminate equations with multiple variables, utilizing Euler's function to express solutions based on coefficients and free term.

Contribution

It introduces a novel explicit formula for solutions to linear indeterminate equations using Euler's function, enhancing understanding of their structure.

Findings

01

Provides a formula for solutions based on coefficients and free term

02

Utilizes Euler's function to derive solutions

03

Clarifies the structure of solutions to linear indeterminate equations

Abstract

In this paper, using Euler's function, we give a formula of all integral solutions to linear indeterminate equation with $s$ -variables $a_{1} x_{1} + a_{2} x_{2} + ... + a_{s} x_{s} = n$ . It is a explicit formula of the coefficients $a_{1}$ , $a_{2}$ ,..., $a_{s}$ and the free term $n$ .

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Taxonomy

TopicsFunctional Equations Stability Results · Fractional Differential Equations Solutions · Iterative Methods for Nonlinear Equations