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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
4 months, 2 weeks 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? · 4 months, 2 weeks ago