MathDB

1/b = sum 1/ n_k

Source: IV - Rioplatense 1995 L3 P4

September 19, 2022

number theory

Problem Statement

Given the natural numbers

a

and

b

, with

1 \le a <b

, prove that there exist natural numbers

n_1<n_2< ...<n_k

, with

k \le a

such that

\frac{a}{b}=\frac{1}{n_1}+\frac{1}{n_2}+...+\frac{1}{n_k}