Glossary math Term Page

linear Diophantine equation

an equation of the form `ax+by=c` with integer solutions

linear-diophantine-equation #math#number-theory

Related Concepts

Bézout's identity greatest common divisor coprime

Core Idea

linear Diophantine equation is an equation of the form ax+by=c with integer solutions. It usually makes the most sense alongside Bézout's identity, greatest common divisor, coprime.

Why It Matters Here

Mathbong reuses this term across number-theory posts as shared vocabulary.

Posts Mentioning This Concept

[Introduction to Number Theory Series Part 6] How Does Bézout's Identity Express the GCD as a Formula? See why the gcd is not only a divisor but also a number that can be written in the form ax+by.[정수론 입문 시리즈 6편] 베주 항등식은 최대공약수를 어떻게 식으로 보여 줄까? 베주 항등식을 통해 최대공약수가 단순한 수가 아니라 ax+by 꼴로 표현되는 구조라는 점을 정리합니다.[Introduction to Number Theory Series Part 7] When Does a Linear Diophantine Equation Have Integer Solutions? Learn the exact condition for ax+by=c to have integer solutions through the gcd and Bézout's identity.