\[ \lfloor a \rfloor bc = 3 \\ a \lfloor b \rfloor c = 4 \\ ab \lfloor c \rfloor = 5 \]
If \(a,b\) and \(c\) are real numbers satisfying the system of equations above. Find all solutions of \((a,b,c) \).
Notation: \( \lfloor \cdot \rfloor \) denotes the floor function.
I wasn't able to find all the solutions, so i request the community to provide the total solutions.