Algebra · Floor function · Fractional part · Systems of equations
Solve the system of equations
\[ \begin{aligned} x - y &= 2005, \\ \lfloor x \rfloor + \lfloor y \rfloor &= 2007, \end{aligned} \]
where \(\lfloor t \rfloor\) denotes the integer part of the real number \(t\).
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Serbian Municipal Competition 2007, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source