Classical Inequalities addicts can do this. Part 1

Algebra Level 5

\[\begin{cases}\begin{align} x_{1} + x_{2} + x_{3} + \cdots + x_{n} &= 2016 \\\\ x_{1}^{4} + x_{2}^{4} + x_{3}^{4} + \cdots + x_{n}^{4} &= 2016\times 512 \end{align}\end{cases}\]

Let \(x_1, x_2, \ldots , x_n \) be real numbers.

Find the smallest possible value of \(n\) such that there exists real solutions to the equations above.


For more problems like this, try answering this set .

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