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2001 Moldova National Olympiad
Problem 4
Im((a+b)(b+c)(c+a)/abc)
Im((a+b)(b+c)(c+a)/abc)
Source: 2001 Moldova MO Grade 8 P4
April 12, 2021
number theory
Problem Statement
Find all integers that can be written as
(
a
+
b
)
(
b
+
c
)
(
c
+
a
)
a
b
c
\frac{(a+b)(b+c)(c+a)}{abc}
ab
c
(
a
+
b
)
(
b
+
c
)
(
c
+
a
)
, where
a
,
b
,
c
a,b,c
a
,
b
,
c
are pairwise coprime positive integers.
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