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Austrian MO National Competition
2005 Federal Competition For Advanced Students, Part 2
1
LCM(a,b,c) = a+b+c
LCM(a,b,c) = a+b+c
Source: Austrian MO 2005 round 2
June 27, 2005
number theory
least common multiple
number theory unsolved
Problem Statement
Find all triples
(
a
,
b
,
c
)
(a,b,c)
(
a
,
b
,
c
)
of natural numbers, such that
L
C
M
(
a
,
b
,
c
)
=
a
+
b
+
c
LCM(a,b,c)=a+b+c
L
CM
(
a
,
b
,
c
)
=
a
+
b
+
c
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