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simultaneous floor equations

\[ \lfloor a \rfloor bc = 3 \\ a \lfloor b \rfloor c = 4 \\ ab \lfloor c \rfloor = 5 \]

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.

Note by Raghav Rathi
11 months, 1 week ago

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(√[20/3] , -√[15/4] , -√[3/5]) is the only one I could find. Could you tell me what you did have before asking it here?

Saya Suka - 11 months, 1 week ago

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