# Dedicated to $$e^{i\pi} + 1729$$

$\left(\sum_{n=1}^{10000} 2S_m + 5S_n\right)^{1729}$

Let $$S_n$$ and $$S_m$$ be two natural numbers for arbitary natural numbers $$n$$ and $$m$$ : such that , $$S_{n-1}=2S_{m+1}$$.Also $$5^m | S_m$$ , provided that $$(n,m) \leq 10000$$.

Then evaluate above sumation modulo 10

Bonus : Generalize this.

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