MathDB

A/B+C/D = E/F , F=lcm(BD), d/E, D/F, prove d/B and d/B

Source: 2001 Estonia National Olympiad Final Round grade 11 p2

March 12, 2020

least common multipledividesdivisornumber theory

Problem Statement

A student wrote a correct addition operation

A/B+C/D = E/F

on the blackboard, where both summands are irreducible and

F

is the least common multiple of

B

and

D

. After that, the student reduced the sum

E/F

correctly by an integer

d

. Prove that

d

is a common divisor of

B

and

D