Difference between revisions of "Template:AotD"

Revision as of 18:05, 17 December 2007

Diophantine equation

This article was also a AoPSWiki word of the week

A Diophantine equation is an multi-variable equation for which integer solutions (or sometimes natural number or whole number solutions) are to be found.
Finding the solution or solutions to a Diophantine equation is closely tied to modular arithmetic and number theory. Often, when a Diophantine equation has infinitely many solutions, parametric form is used to express the relation between the variables of the equation.
Diophantine equations are named for the ancient Greek/Alexandrian mathematician Diophantus.
A Diophantine equation in the form $ax+by=c$ is known as a linear combination. If two relatively prime integers $a$ and $b$ are written in this form with $c=1$ , the equation will have an infinite number of solutions. More generally, there will always be an... [more]

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-===[[Fibonacci sequence]]===
+===[[Diophantine equation]]===
 {{WotWAlso}}
-The '''Fibonacci sequence''' is a [[sequence]] of [[integer]]s in which the first and second terms are both equal to 1 and each subsequent term is the sum of the two preceding it.  The first few terms are <math>1, 1, 2, 3, 5, 8, 13, 21, 34, 55,...</math>.
+A '''Diophantine equation''' is an multi-variable [[equation]] for which [[integer]] solutions (or sometimes [[natural number]] or [[whole number]] solutions) are to be found.
-The Fibonacci sequence can be written [[recursion|recursively]] as <math>F_1 = F_2 = 1</math> and <math>F_n=F_{n-1}+F_{n-2}</math> for <math>n \geq 3</math>.  This is the simplest nontrivial... [[Fibonacci sequence|[more]]]
+Finding the solution or solutions to a Diophantine equation is closely tied to [[modular arithmetic]] and [[number theory]]. Often, when a Diophantine equation has infinitely many solutions, [[parametric form]] is used to express the relation between the variables of the equation.
+Diophantine equations are named for the ancient Greek/Alexandrian mathematician Diophantus.
+A Diophantine equation in the form <math>ax+by=c</math> is known as a linear combination.  If two [[relatively prime]] integers <math>a</math> and <math>b</math> are written in this form with <math>c=1</math>, the equation will have an infinite number of solutions.  More generally, there will always be an... [[Diophantine equation|[more]]]
 </blockquote>

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Difference between revisions of "Template:AotD"

Revision as of 18:05, 17 December 2007

Diophantine equation