# Let's play with sums!

Algebra Level 4

If $$x_{1}$$ and $$x_{2}$$ are distinct roots of $$x^{2}-6x+1=0$$ and $$S_{n}=x_{1}^{n}+x_{2}^{n}$$, where $$n$$ is a positive integer. Find the remainder of $$S_{50}$$ when divided by 5.

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