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JOM 2024
5
5
Part of
JOM 2024
Problems
(1)
3 perfect squares
Source: JOM 2024 P5
2/29/2024
Do there exist infinitely many triplets of positive integers
(
a
,
b
,
c
)
(a, b, c)
(
a
,
b
,
c
)
such that the following two conditions hold: 1.
gcd
(
a
,
b
,
c
)
=
1
\gcd(a, b, c) = 1
g
cd
(
a
,
b
,
c
)
=
1
; 2.
a
+
b
+
c
,
a
2
+
b
2
+
c
2
a+b+c, a^2+b^2+c^2
a
+
b
+
c
,
a
2
+
b
2
+
c
2
and
a
b
c
abc
ab
c
are all perfect squares?(Proposed by Ivan Chan Guan Yu)
number theory