# Let Our Powers Combine

Algebra Level 5

Find the largest integer $$n$$, such that if $$\{ x_i \} _{i=1}^n$$ are non-negative real numbers such that

$x_1 ^ 6 + x_2 ^ 6 + \ldots + x_n ^ 6 = n,$

then we will have

$x_1 ^2 + x_2 ^ 2 + \ldots + x_n ^ 2 \leq x_1 ^ 5 + x_2 ^ 5 + \ldots + x_n ^ 5.$

Details and assumptions

The second condition is true for all sets which satisfy the first condition. You are not asked to find just 1 set of numbers which satisfies both conditions.

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