Classical Inequalities addicts can do this. Part 1

Algebra Level 5

{x1+x2+x3++xn=2016x14+x24+x34++xn4=2016×512\begin{cases}\begin{aligned} 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{aligned}\end{cases}

Let x1,x2,,xnx_1, x_2, \ldots , x_n be real numbers.

Find the smallest possible value of nn such that there exists real solutions to the equations above.


For more problems like this, try answering this set .

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