Re: question regarding diofantine equations

In article <1176237012.557078.287790@xxxxxxxxxxxxxxxxxxxxxxxxxx>,
"laura" <laura.brandusan@xxxxxxxxx> wrote:
I want to solve diofantine equations of form:

ax+by=c,

where a, b and c are real numbers and

x and y are natural numbers (>=0).


Are there any methods for solving this ? I don't want to enumerate all
possible pairs (x,y) and to check which ones are good.

Or, is there possible to decide if the equation has solutions without
solving it?

The algorithm is called the extended euclidean algorithm, and one
implementation is the Euclid-Wallis Algorithm:

<http://www.whim.org/nebula/math/euclid-wallis.html>

Rob Johnson <rob@xxxxxxxxxxxxxx>
take out the trash before replying
to view any ASCII art, display article in a monospaced font
.

Relevant Pages

  • Re: question regarding diofantine equations
    ... Are there any methods for solving this? ... The algorithm is called the extended euclidean algorithm, ... element (equivalently, a/b is not rational). ...
    (sci.math)
  • Re: question regarding diofantine equations
    ... In article, rob@xxxxxxxxxxxxxx (Rob Johnson) ... Are there any methods for solving this? ... The algorithm is called the extended euclidean algorithm, ... an extension of Euclid's algorithm to decide whether, say, gamma ...
    (sci.math)