디오판투스 방정식

수학노트
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개요[편집]

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


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역사[편집]


메모[편집]


관련된 항목들[편집]


수학용어번역[편집]

사전 형태의 자료[편집]


리뷰, 에세이, 강의노트[편집]

  • 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[편집]


노트[편집]

위키데이터[편집]

말뭉치[편집]

  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[편집]

메타데이터[편집]

위키데이터[편집]