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p divides m if m/n= sum 1/(i-1)

Source: Chile Finals 2005 L2 p2

October 3, 2022
number theorydivides

Problem Statement

Let pp be a prime number greater than 22 and let m,nm, n be integers such that: mn=1+12+13+...+1p−1.\frac{m}{n}=1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{p-1}. Prove that pp divides mm.
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