Diophantine equation

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A Diophantine equation is an equation which must be solved using only integers. For instance, the Diophantine equation

$4a+3b=10$

has infinitely many solutions, two of which are $(1,2)$ and $(4,-2)$.

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.

See also

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