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Problems
Contests
National and Regional Contests
PEN Problems
PEN A Problems
113
113
Part of
PEN A Problems
Problems
(1)
A 113
Source:
5/25/2007
Find all triples
(
l
,
m
,
n
)
(l, m, n)
(
l
,
m
,
n
)
of distinct positive integers satisfying
gcd
(
l
,
m
)
2
=
l
+
m
,
gcd
(
m
,
n
)
2
=
m
+
n
,
and
gcd
(
n
,
l
)
2
=
n
+
l
.
{\gcd(l, m)}^{2}= l+m, \;{\gcd(m, n)}^{2}= m+n, \; \text{and}\;\;{\gcd(n, l)}^{2}= n+l.
g
cd
(
l
,
m
)
2
=
l
+
m
,
g
cd
(
m
,
n
)
2
=
m
+
n
,
and
g
cd
(
n
,
l
)
2
=
n
+
l
.
number theory
relatively prime
Divisibility Theory