Re: question regarding diofantine equations

In article <20070410.142106@xxxxxxxx>, rob@xxxxxxxxxxxxxx (Rob Johnson)
wrote:

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>

OP wants a, b, and c to be real numbers. If b = 1 and c = 0
then the question of whether a x + b y = c has solutions is
the question of whether a is rational. It's going to take a heck of
an extension of Euclid's algorithm to decide whether, say, gamma
is rational.

--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)
.

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