"디오판투스 방정식"의 두 판 사이의 차이

수학노트
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==개요==
  
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* 다변수다항식의 정수해 또는 유리수해를 찾는 문제를 디오판투스 방정식이라 함
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* 부정방정식으로도 불림
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==예==
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* <math>x^n+y^n=z^n</math>의 정수해에 대한 [[페르마의 마지막 정리]]가 유명한 예
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* <math>x^2-dy^2=\pm 1</math> 형태의 [[펠 방정식(Pell's equation)|펠 방정식]]은 초등정수론과 대수적수론에서 중요한 역할을 함
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* <math>x^3+y^3=1729</math>의 정수해. [[라마누잔과 1729]] 참조
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* <math>3x^3+4y^3+5z^3=0</math> ([http://www.math.lsu.edu/%7Everrill/teaching/math7280/selmer_example/selmer_example.pdf http://www.math.lsu.edu/~verrill/teaching/math7280/selmer_example/selmer_example.pdf])
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* [[합동수 문제 (congruent number problem)]]
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* [[사각 피라미드 퍼즐]]
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* [[펠 방정식(Pell's equation)]]
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* [[피타고라스 쌍(Pythagorean triple)]]
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* [[라마누잔-나겔 방정식]]
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==역사==
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* [[수학사 연표]]
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==메모==
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* [[모델 추측 (Mordell conjecture)]]
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==관련된 항목들==
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* [[페르마의 마지막 정리]]
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* [[타원곡선]]
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* [[대수적수론]]
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* [[라마누잔과 1729]]
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==수학용어번역==
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* {{학술용어집|url=diophantine}}
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* [http://kms.or.kr/home/kor/board/bulletin_list_subject.asp?bulletinid=%7BD6048897-56F9-43D7-8BB6-50B362D1243A%7D&boardname=%BC%F6%C7%D0%BF%EB%BE%EE%C5%E4%B7%D0%B9%E6&globalmenu=7&localmenu=4 대한수학회 수학용어한글화 게시판]
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==사전 형태의 자료==
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* http://ko.wikipedia.org/wiki/디오판투스방정식
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* http://en.wikipedia.org/wiki/Diophantine_equation
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* http://en.wikipedia.org/wiki/Thue-Siegel-Roth_theorem
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* {{매스월드|urlname=DiophantineEquation|title=디오판투스 방정식}}
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* http://mathworld.wolfram.com/DiophantineEquation.html
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==리뷰, 에세이, 강의노트==
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* 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.
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* 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.
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* Ono, Ken. “Ramanujan, Taxicabs, Birthdates, ZIP Codes, and Twists.” The American Mathematical Monthly 104, no. 10 (December 1997): 912. doi:10.2307/2974471.
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==관련도서==
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* [http://books.google.com/books?id=QugvF7xfE-oC Diophantine equations]
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** Mordell, L. J. (1969)
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== 노트 ==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q905896 Q905896]
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===말뭉치===
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# Diophantine equation, equation involving only sums, products, and powers in which all the constants are integers and the only solutions of interest are integers.<ref name="ref_620634e0">[https://www.britannica.com/science/Diophantine-equation Diophantine equation | mathematics]</ref>
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# Congruence methods provide a useful tool in determining the number of solutions to a Diophantine equation.<ref name="ref_620634e0" />
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# 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.<ref name="ref_6745cace">[https://math.libretexts.org/Courses/Mount_Royal_University/MATH_2150%3A_Higher_Arithmetic/5%3A_Diophantine_Equations/5.1%3A_Linear_Diophantine_Equations 5.1: Linear Diophantine Equations]</ref>
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# : Solve the Homogeneous linear Diophantine equation \(6x+9y=0, x, y \in \mathbb{Z}\).<ref name="ref_6745cace" />
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# Use the following steps to solve a non-homogeneous linear Diophantine equation.<ref name="ref_6745cace" />
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# Finding the solution or solutions to a Diophantine equation is closely tied to modular arithmetic and number theory.<ref name="ref_bbcbc179">[https://artofproblemsolving.com/wiki/index.php/Diophantine_equation Art of Problem Solving]</ref>
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# A Diophantine equation in the form is known as a linear combination.<ref name="ref_bbcbc179" />
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# The solutions to the diophantine equation correspond to lattice points that lie on the line.<ref name="ref_bbcbc179" />
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# Sometimes, modular arithmetic can be used to prove that no solutions to a given Diophantine equation exist.<ref name="ref_bbcbc179" />
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# A linear Diophantine equation is an equation of the first-degree whose solutions are restricted to integers.<ref name="ref_de913260">[https://medium.com/cantors-paradise/famous-diophantine-equations-84073467d366 Famous Diophantine Equations]</ref>
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# This Diophantine equation was first studied extensively by Indian mathematician Brahmagupta around the year 628.<ref name="ref_de913260" />
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# A linear Diophantine equation equates to a constant the sum of two or more monomials, each of degree one.<ref name="ref_31d5bbbd">[https://en.wikipedia.org/wiki/Diophantine_equation Diophantine equation]</ref>
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# The simplest linear Diophantine equation takes the form ax + by = c, where a, b and c are given integers.<ref name="ref_31d5bbbd" />
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# A homogeneous Diophantine equation is a Diophantine equation that is defined by a homogeneous polynomial.<ref name="ref_31d5bbbd" />
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# If a Diophantine equation has as an additional variable or variables occurring as exponents, it is an exponential Diophantine equation.<ref name="ref_31d5bbbd" />
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# 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.<ref name="ref_97214d62">[https://docs.sympy.org/latest/modules/solvers/diophantine.html Diophantine — SymPy 1.7.1 documentation]</ref>
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# Hilbert's 10th problem asked if an algorithm existed for determining whether an arbitrary Diophantine equation has a solution.<ref name="ref_eb00bace">[https://mathworld.wolfram.com/DiophantineEquation.html Diophantine Equation -- from Wolfram MathWorld]</ref>
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# We exhibit a collection of (probably infinitely many) rational numbers k for which this Diophantine equation is satisfied.<ref name="ref_ab53d062">[http://ijmsi.ir/article-1-1004-en.html On the Diophantine Equation x^6+ky^3=z^6+kw^3]</ref>
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# Brindza, B.: On a diophantine equation connected with the Fermat equation.<ref name="ref_9700b534">[http://www.numdam.org/item/CM_1987__61_2_137_0/ Zeros of polynomials and exponential diophantine equations]</ref>
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===소스===
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<references />
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[[분류:디오판투스 방정식]]
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==메타데이터==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q905896 Q905896]
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===Spacy 패턴 목록===
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* [{'LOWER': 'diophantine'}, {'LEMMA': 'equation'}]
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* [{'LOWER': 'diophantic'}, {'LEMMA': 'equation'}]

2021년 2월 17일 (수) 05:03 기준 최신판

개요

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


예


역사


메모


관련된 항목들


수학용어번역

사전 형태의 자료


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.

관련도서


노트

위키데이터

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]

소스

  1. ↑ 이동: 1.0 1.1 Diophantine equation | mathematics
  2. ↑ 이동: 2.0 2.1 2.2 5.1: Linear Diophantine Equations
  3. ↑ 이동: 3.0 3.1 3.2 3.3 Art of Problem Solving
  4. ↑ 이동: 4.0 4.1 Famous Diophantine Equations
  5. ↑ 이동: 5.0 5.1 5.2 5.3 Diophantine equation
  6. ↑ Diophantine — SymPy 1.7.1 documentation
  7. ↑ Diophantine Equation -- from Wolfram MathWorld
  8. ↑ On the Diophantine Equation x^6+ky^3=z^6+kw^3
  9. ↑ Zeros of polynomials and exponential diophantine equations

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LOWER': 'diophantine'}, {'LEMMA': 'equation'}]
  • [{'LOWER': 'diophantic'}, {'LEMMA': 'equation'}]
원본 주소 "https://wiki.mathnt.net/index.php?title=디오판투스_방정식&oldid=52243"