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In mathematics, a Diophantine equation is an equation, ... Archimedes's cattle problem and the monkey and the coconuts. 17th and 18th centuries. In 1637, ...
Archimedes's cattle problem (or the problema bovinum or problema Archimedis) is a problem in Diophantine analysis, the study of polynomial equations with integer solutions. Attributed to Archimedes , the problem involves computing the number of cattle in a herd of the sun god from a given set of restrictions.
Archimedes challenges them to count the numbers of cattle in the Herd of the Sun by solving a number of simultaneous Diophantine equations. There is a more difficult version of the problem in which some of the answers are required to be square numbers .
In mathematics, Diophantine geometry is the study of Diophantine equations by means of powerful methods in algebraic geometry. By the 20th century it became clear for some mathematicians that methods of algebraic geometry are ideal tools to study these equations. [1] Diophantine geometry is part of the broader field of arithmetic geometry.
This category corresponds roughly to MSC 11Dxx Diophantine equations; see 11Dxx at MathSciNet and 11Dxx at zbMATH. Subcategories This category has the following 4 subcategories, out of 4 total.
8.2 Diophantine equations. 8.3 Sieve theory. 9 Probability theory. ... Archimedes's lemmas; Johnson–Lindenstrauss lemma (Euclidean geometry) Hyperbolic geometry
Pell's equation, also called the Pell–Fermat equation, is any Diophantine equation of the form =, where n is a given positive nonsquare integer, and integer solutions are sought for x and y. In Cartesian coordinates , the equation is represented by a hyperbola ; solutions occur wherever the curve passes through a point whose x and y ...
Equations in the book are presently called Diophantine equations. The method for solving these equations is known as Diophantine analysis. Most of the Arithmetica problems lead to quadratic equations. In Book 3, Diophantus solves problems of finding values which make two linear expressions simultaneously into squares or cubes.