Diophantine equation: Difference between revisions
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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]]. | 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]]. | ||
Revision as of 14:28, 6 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 , which may be solved by means of the extended Euclidean algorithm.
