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Pan African
2006 Pan African
2
2
Part of
2006 Pan African
Problems
(1)
Which integers are (a/b+b/c+c/a) and (b/a+a/c+c/b)?
Source: Pan African MO 2006 Q2
5/1/2013
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be three non-zero integers. It is known that the sums
a
b
+
b
c
+
c
a
\frac{a}{b}+\frac{b}{c}+\frac{c}{a}
b
a
+
c
b
+
a
c
and
b
a
+
c
b
+
a
c
\frac{b}{a}+\frac{c}{b}+\frac{a}{c}
a
b
+
b
c
+
c
a
are integers. Find these sums.
Vieta
algebra
polynomial
Rational Root Theorem
number theory unsolved
number theory