MathDB
Harmonic numbers and prime divisors

Source: Czech and Slovak Olympiad 1970, National Round, Problem 1

July 4, 2024
number theoryprimeprime divisorsFractionsharmonicnumbers

Problem Statement

Let p>2p>2 be a prime and a,ba,b positive integers such that ab=1+12+13+⋯+1p−1.\frac ab=1+\frac12+\frac13+\cdots+\frac{1}{p-1}. Show that pp is a divisor of a.a.
Back to ProblemsView on AoPS