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All-Russian Olympiad Regional Round
1996 All-Russian Olympiad Regional Round
9.3
9.3
Part of
1996 All-Russian Olympiad Regional Round
Problems
(1)
(a + b)(b + c)(c + a)/ abc is integer - All-Russian MO 1996 Regional (R4) 9.3
Source:
9/23/2024
Let
a
,
b
a, b
a
,
b
and
c
c
c
be pairwise relatively prime natural numbers. Find all possible values of
(
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
)
if known what it is integer.
number theory
Integer