# Large Exponents

Let $$x$$ be defined as follows: $$x = 1^{2013} + 2^{2013} + 3^{2013} + \ldots + 2014^{2013}$$

And for every $$i$$, let $$Z_i$$ be the smallest non-negative integer such that: $$x \equiv Z_i \pmod{i}$$

Calculate the value of $$2 \cdot Z_{2013} + Z_{2014} + 5 \cdot Z_{2015} - 100 \cdot Z_{2016}$$

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