I am studying linear Diophantine equations with real coefficients: \begin{equation} ax+by=1\qquad a,b\in\mathbb{R} \end{equation} I have no clue about where to begin; could someone please point me to some starting point? I was not able to find anything in the question database.

  • $\begingroup$ $x, y$ should be integers while $a,b$ are real? $\endgroup$ – Bernard Nov 24 '15 at 20:49
  • $\begingroup$ Exactly, for instance $\pi\cdot 2+(1/2-\pi)\cdot 2=1$ $\endgroup$ – marco trevi Nov 24 '15 at 20:51

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