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National and Regional Contests
Mexico Contests
Mexico National Olympiad
2010 Mexico National Olympiad
1
abc = a+b+c+1
abc = a+b+c+1
Source: Mexican National Olympiad 2010 Problem 1
July 15, 2014
number theory proposed
number theory
Problem Statement
Find all triplets of natural numbers
(
a
,
b
,
c
)
(a,b,c)
(
a
,
b
,
c
)
that satisfy the equation
a
b
c
=
a
+
b
+
c
+
1
abc=a+b+c+1
ab
c
=
a
+
b
+
c
+
1
.
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