question regarding diofantine equations

Hi,


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?

thanks.
Laura

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