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National and Regional Contests
Moldova Contests
Moldova Team Selection Test
2017 Moldova Team Selection Test
4
4
Part of
2017 Moldova Team Selection Test
Problems
(1)
n of the form...
Source: Moldova TST 2017, B4
3/6/2017
Determine all natural numbers
n
n
n
of the form
n
=
[
a
,
b
]
+
[
b
,
c
]
+
[
c
,
a
]
n=[a,b]+[b,c]+[c,a]
n
=
[
a
,
b
]
+
[
b
,
c
]
+
[
c
,
a
]
where
a
,
b
,
c
a,b,c
a
,
b
,
c
are positive integers and
[
u
,
v
]
[u,v]
[
u
,
v
]
is the least common multiple of the integers
u
u
u
and
v
v
v
.
number theory