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Question Number 167367 by mnjuly1970 last updated on 14/Mar/22

Commented by mr W last updated on 15/Mar/22

for a=2 there is no solution. for any  other values of a>1 there is always  solution, i think.

$${for}\:{a}=\mathrm{2}\:{there}\:{is}\:{no}\:{solution}.\:{for}\:{any} \\ $$$${other}\:{values}\:{of}\:{a}>\mathrm{1}\:{there}\:{is}\:{always} \\ $$$${solution},\:{i}\:{think}. \\ $$

Answered by TheSupreme last updated on 15/Mar/22

0<x<1 ⌊(a^2 −a)x⌋=2  1≤x<2 ⌊(a^2 −a)x⌋=1  x≥2 no solution

$$\mathrm{0}<{x}<\mathrm{1}\:\lfloor\left({a}^{\mathrm{2}} −{a}\right){x}\rfloor=\mathrm{2} \\ $$$$\mathrm{1}\leqslant{x}<\mathrm{2}\:\lfloor\left({a}^{\mathrm{2}} −{a}\right){x}\rfloor=\mathrm{1} \\ $$$${x}\geqslant\mathrm{2}\:{no}\:{solution} \\ $$

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