MathDB
Sequence of Numbers

Source:

January 5, 2007
number theoryrelatively primeAIMEAIME 2000

Problem Statement

A sequence of numbers x1,x2,x3,…,x100x_{1},x_{2},x_{3},\ldots,x_{100} has the property that, for every integer kk between 11 and 100,100, inclusive, the number xkx_{k} is kk less than the sum of the other 9999 numbers. Given that x50=m/n,x_{50}=m/n, where mm and nn are relatively prime positive integers, find m+n.m+n.
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