MathDB

0252 number theory 2nd edition Round 5 p2

Source:

May 10, 2021

number theory2nd edition

Problem Statement

Let S be the set of positive integers

n

for which

\frac{3}{n}

cannot be written as the sum of two rational numbers of the form

\frac{1}{k}

, where

k

is a positive integer. Prove that

S

cannot be written as the union of finitely many arithmetic progressions.