# Not enough information for AM-GM

Calculus Level 5

Let $$s_1, \ldots, s_n$$, with $$n$$ being an integer $$\geq 1$$, be a series of positive real numbers such that

$\displaystyle \sum_{i=1}^n s_i = 271.$

If the maximum value of

$\displaystyle \prod_{k=1}^n s_k = \dfrac {a^x}{b^y}$

where $$a$$ and $$b$$ are square-free coprime positive integers, and $$x$$ and $$y$$ being positive integers greater than 1, find $$a+x+b+y$$.

Note: $$n$$ is variable.

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