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Balkan MO
2006 Balkan MO
3
3
Part of
2006 Balkan MO
Problems
(1)
Nice result of divisibility
Source: Balkan MO 2006, Problem 3 - own
4/29/2006
Find all triplets of positive rational numbers
(
m
,
n
,
p
)
(m,n,p)
(
m
,
n
,
p
)
such that the numbers
m
+
1
n
p
m+\frac 1{np}
m
+
n
p
1
,
n
+
1
p
m
n+\frac 1{pm}
n
+
p
m
1
,
p
+
1
m
n
p+\frac 1{mn}
p
+
mn
1
are integers. Valentin Vornicu, Romania
number theory proposed
number theory