# SAT1000 - P873

Algebra Level pending

If there exists $t \in \mathbb R$, so that the following system of $n$ equations all holds:

\begin{cases} \begin{aligned} \lfloor t \rfloor & = 1 \\ \lfloor t^2 \rfloor & = 2 \\ \lfloor t^3 \rfloor & = 3 \\ & \vdots \\ \lfloor t^n \rfloor & = n \end{aligned} \end{cases}

Then find the maximum of positive integer $n$.

Have a look at my problem set: SAT 1000 problems

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