# 11's remainders

Let $$\displaystyle S_1=\sum_{n=6}^{10} (2n+1)^{n-5}$$ and $$\displaystyle S_2=\sum_{n=6}^{10} (2n)^{n-5}$$.

When $$S_1$$ and $$S_2$$ are divided by 11, they leave remainders $$a$$ and $$b$$ respectively.

Find the remainder when $$a^4b^4$$ is divided by 11.

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