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[ x ] + {y } =z, [ y ] + {z } =x, [ z ] + {x } =y

Source: 2005 Austria Beginners' Competition p3

October 12, 2022

floor functionsystem of equationsSystemalgebra

Problem Statement

Determine all triples

(x,y,z)

of real numbers that satisfy all of the following three equations:

\begin{cases} \lfloor x \rfloor + \{y\} =z \\ \lfloor y \rfloor + \{z\} =x \\ \lfloor z \rfloor + \{x\} =y \end{cases}