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Regional Mathematical Olympiad
2005 India Regional Mathematical Olympiad
6
Triples
Triples
Source: Indian RMO 2005 Problem 6
February 28, 2006
Problem Statement
Determine all triples of positive integers
(
a
,
b
,
c
)
(a,b,c)
(
a
,
b
,
c
)
such that
a
≤
b
≤
c
a \leq b \leq c
a
≤
b
≤
c
and
a
+
b
+
c
+
a
b
+
b
c
+
c
a
=
a
b
c
+
1
a +b + c + ab+ bc +ca = abc +1
a
+
b
+
c
+
ab
+
b
c
+
c
a
=
ab
c
+
1
.
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