MathDB

TOT 445 1995 Spring A J1 a/b+b/c+c/a and a/c+c/b+b/a are integers

Source:

July 9, 2024

number theory

Problem Statement

Prove that if

a

b

and

c

are integers and the sums

\frac{a}{b}+\frac{b}{c}+\frac{c}{a} \,\,\,\, and \,\,\,\, \frac{a}{c}+\frac{c}{b}+\frac{b}{a}

are also integers, then we have

|a| = |v| = |c|

.
(A Gribalko)