# 1000 Followers problem!

Algebra Level 5

$\large \alpha^{\eta} - \alpha^2-\alpha-\eta=0$

Consider the above polynomial and let its roots be $$\large\beta_{(1,\eta)},\beta_{(2,\eta)},\beta_{(3,\eta)} , \ldots, \beta_{(\eta,\eta)}$$.

Define $$\large S_{\eta}= \displaystyle\sum_{i=1}^{\eta} \beta_{(i,\eta)}^{\eta}$$, find the value of $$\large \displaystyle\sum_{j=5}^{1000} S_j$$.

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