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Let ${x}$ and $[x]$ denote the fractional part of $x$ and the greatest integer $\leq x$ respectively of a real number $x$. If $\int_0^n {x},dx$, $\int_0^n [x],dx$ and $10(n^2 - n)$, $(n \in \mathbb{N}, n > 1)$ are three consecutive terms of a G.P., then $n$ is equal to ______.
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