MathDB

Nice lcm number theory

Source: 44th International Tournament of Towns, Senior A-Level P2, Fall 2022

February 16, 2023

number theoryTournament of Towns

Problem Statement

Consider two coprime integers

p{}

and

q{}

which are greater than

1{}

and differ from each other by more than

1{}

. Prove that there exists a positive integer

n{}

such that

\text{lcm}(p+n, q+n)<\text{lcm}(p,q).