Algebra · Floor function · Functional equations · Real numbers
Find all pairs of real numbers \(a\) and \(b\) such that the equality
\[ \lfloor ax + by \rfloor + \lfloor bx + ay \rfloor = (a+b)\lfloor x+y \rfloor \]
holds for all real numbers \(x\) and \(y\).
(For a real number \(t\), the symbol \(\lfloor t \rfloor\) denotes the greatest integer that is not greater than \(t\).)
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Serbian Municipal Competition 2019, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source