MathDB

1/a_1 + 2/a_2 +...+ n/a_n = (a_1 + a_2 +... + a_n)/ 2

Source: 2010 Grand Duchy of Lithuania, Mathematical Contest p2 (Baltic Way TST)

October 3, 2020

number theorydiophantineDiophantine equation

Problem Statement

Find all positive integers

n

for which there are distinct integer numbers

a_1, a_2, ... , a_n

such that

\frac{1}{a_1}+\frac{2}{a_2}+...+\frac{n}{a_n}=\frac{a_1 + a_2 + ... + a_n}{2}