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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