Diophantine equation: Difference between revisions
Jump to navigation
Jump to search
imported>Josy Shewell Brockway (New page: A ''Diophantine equation'', named after the Ancient Greek mathematician Diophantus, is an equation in any number of variables that only admits solutions from the...) |
imported>Todd Coles (subpages) |
||
| (3 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
A ''Diophantine equation'', named after the [[Ancient Greece|Ancient Greek]] mathematician [[Diophantus]], is an [[equation]] in any number of variables that only admits solutions from the [[ring]] of [[integers]], <math>\mathbb Z</math>. Their study forms a part of the branch of [[mathematics]] known as [[number theory]]. | {{subpages}} | ||
A '''Diophantine equation''', named after the [[Ancient Greece|Ancient Greek]] mathematician [[Diophantus]], is an [[equation]] in any number of variables that only admits solutions from the [[ring (mathematics)|ring]] of [[integers]], <math>\mathbb Z</math>. Their study forms a part of the branch of [[mathematics]] known as [[number theory]]. | |||
Of particular interest are linear Diophantine equations, of the form <math>a_1x_1+a_2x_2+\cdots+a_nx_n=b</math>, which may be solved by means of the extended [[Euclidean algorithm]]. | Of particular interest are linear Diophantine equations, of the form <math>a_1x_1+a_2x_2+\cdots+a_nx_n=b</math>, which may be solved by means of the extended [[Euclidean algorithm]]. | ||
Latest revision as of 19:39, 7 April 2009
A Diophantine equation, named after the Ancient Greek mathematician Diophantus, is an equation in any number of variables that only admits solutions from the ring of integers, . Their study forms a part of the branch of mathematics known as number theory.
Of particular interest are linear Diophantine equations, of the form Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a_1x_1+a_2x_2+\cdots+a_nx_n=b} , which may be solved by means of the extended Euclidean algorithm.