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a/b+b/c+c/a and a/c+b/a+c/b are both integers

Source: Indian Postal Coaching 2007 set 6 p2

May 25, 2020

Integersnumber theoryalgebra

Problem Statement

Let

a, b, c

be nonzero integers such that

M = \frac{a}{b}+\frac{b}{c}+\frac{c}{a}

and

N =\frac{a}{c}+\frac{b}{a}+\frac{c}{b}

are both integers. Find

M

and

N

.

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