# Are you smarter than an 8th grader? #2

Number Theory Level 4

Given that $$a$$ has a remainder of $$6$$ and $$b$$ has a remainder of $$1$$ when divided by $$14$$, what is the remainder of $$x$$ when divided by $$14$$, given $$x$$ is an integer solution to $$x^{2}-2ax+b=0$$

###### This problem is part of the question set Mathematics in Anime. It appears in the anime Puella Magi Madoka Magica. Students attending the Math class are only $$14$$ years old, yet they are expected to solve this question on the spot!
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