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National and Regional Contests
PEN Problems
PEN H Problems
77
77
Part of
PEN H Problems
Problems
(1)
H 77
Source:
5/25/2007
Find all pairwise relatively prime positive integers
l
,
m
,
n
l, m, n
l
,
m
,
n
such that
(
l
+
m
+
n
)
(
1
l
+
1
m
+
1
n
)
(l+m+n)\left( \frac{1}{l}+\frac{1}{m}+\frac{1}{n}\right)
(
l
+
m
+
n
)
(
l
1
+
m
1
+
n
1
)
is an integer.
ratio
number theory
relatively prime
Diophantine Equations