# 디오판투스 방정식

둘러보기로 가기 검색하러 가기

## 개요

• 다변수다항식의 정수해 또는 유리수해를 찾는 문제를 디오판투스 방정식이라 함
• 부정방정식으로도 불림

## 리뷰, 에세이, 강의노트

• Pannekoek, René. “Diophantus Revisited: On Rational Surfaces and K3 Surfaces in the Arithmetica.” arXiv:1509.06138 [math], September 21, 2015. http://arxiv.org/abs/1509.06138.
• Das, Pranabesh, and Amos Turchet. “Invitation to Integral and Rational Points on Curves and Surfaces.” arXiv:1407.7750 [math], July 29, 2014. http://arxiv.org/abs/1407.7750.
• Ono, Ken. “Ramanujan, Taxicabs, Birthdates, ZIP Codes, and Twists.” The American Mathematical Monthly 104, no. 10 (December 1997): 912. doi:10.2307/2974471.

## 노트

### 말뭉치

1. Diophantine equation, equation involving only sums, products, and powers in which all the constants are integers and the only solutions of interest are integers.[1]
2. Congruence methods provide a useful tool in determining the number of solutions to a Diophantine equation.[1]
3. Linear Diophantine equation in two variables takes the form of $$ax+by=c,$$ where $$x, y \in \mathbb{Z}$$ and a, b, c are integer constants.[2]
4. : Solve the Homogeneous linear Diophantine equation $$6x+9y=0, x, y \in \mathbb{Z}$$.[2]
5. Use the following steps to solve a non-homogeneous linear Diophantine equation.[2]
6. Finding the solution or solutions to a Diophantine equation is closely tied to modular arithmetic and number theory.[3]
7. A Diophantine equation in the form is known as a linear combination.[3]
8. The solutions to the diophantine equation correspond to lattice points that lie on the line.[3]
9. Sometimes, modular arithmetic can be used to prove that no solutions to a given Diophantine equation exist.[3]
10. A linear Diophantine equation is an equation of the first-degree whose solutions are restricted to integers.[4]
11. This Diophantine equation was first studied extensively by Indian mathematician Brahmagupta around the year 628.[4]
12. A linear Diophantine equation equates to a constant the sum of two or more monomials, each of degree one.[5]
13. The simplest linear Diophantine equation takes the form ax + by = c, where a, b and c are given integers.[5]
14. A homogeneous Diophantine equation is a Diophantine equation that is defined by a homogeneous polynomial.[5]
15. If a Diophantine equation has as an additional variable or variables occurring as exponents, it is an exponential Diophantine equation.[5]
16. We call a “Diophantine equation” to an equation of the form, $$f(x_1, x_2, \ldots x_n) = 0$$ where $$n \geq 2$$ and $$x_1, x_2, \ldots x_n$$ are integer variables.[6]
17. Hilbert's 10th problem asked if an algorithm existed for determining whether an arbitrary Diophantine equation has a solution.[7]
18. We exhibit a collection of (probably infinitely many) rational numbers k for which this Diophantine equation is satisfied.[8]
19. Brindza, B.: On a diophantine equation connected with the Fermat equation.[9]