# linear Diophantine equation with real coefficients

I am studying linear Diophantine equations with real coefficients: $$ax+by=1\qquad a,b\in\mathbb{R}$$ 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.

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