MathDB

a, b and c are perfect squares

Source: 2022 South Russian Girls MO - Assara Seniors p1

March 1, 2024

number theoryPerfect SquaresPerfect Square

Problem Statement

Given three natural numbers

a

b

and

c

. It turned out that they are coprime together. And their least common multiple and their product are perfect squares. Prove that

a

b

and

c

are perfect squares.