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

## 메타데이터

### Spacy 패턴 목록

• [{'LOWER': 'diophantine'}, {'LEMMA': 'equation'}]
• [{'LOWER': 'diophantic'}, {'LEMMA': 'equation'}]