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A special number does not divide an expression

Source: Argentine National Olympiad 2014, Level 3, Problem 5

November 6, 2015
number theoryfactorial

Problem Statement

An integer n≥3n \geq 3 is called special if it does not divide (n−1)!(1+12+⋅⋅⋅+1n−1)\left ( n-1 \right )!\left ( 1+\frac{1}{2}+\cdot \cdot \cdot +\frac{1}{n-1} \right ). Find all special numbers nn such that 10≤n≤10010 \leq n \leq 100.
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