Let's play with sums!

Algebra Level 4

If x1x_{1} and x2x_{2} are distinct roots of x26x+1=0x^{2}-6x+1=0 and Sn=x1n+x2nS_{n}=x_{1}^{n}+x_{2}^{n}, where nn is a positive integer. Find the remainder of S50S_{50} when divided by 5.

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