A Special Sequence - For my Friend Sharky Kesa!

Algebra Level 4

A sequence of numbers x1,x2,,x100x_{1},x_{2},\ldots ,x_{100} has the property that for every integer kk between 1 and 100 inclusive the number xkx_{k} is kk less than the sum of other 99 numbers. Given that x50=mnx_{50}=\dfrac mn, where mm and nn are relatively prime positive integer, find m+nm+n.

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