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Balkan MO
2021 Balkan MO
3
3
Part of
2021 Balkan MO
Problems
(1)
BMO 2021 problem 3
Source: Balkan MO 2021 P3
9/8/2021
Let
a
,
b
a, b
a
,
b
and
c
c
c
be positive integers satisfying the equation
(
a
,
b
)
+
[
a
,
b
]
=
202
1
c
(a, b) + [a, b]=2021^c
(
a
,
b
)
+
[
a
,
b
]
=
202
1
c
. If
∣
a
−
b
∣
|a-b|
∣
a
−
b
∣
is a prime number, prove that the number
(
a
+
b
)
2
+
4
(a+b)^2+4
(
a
+
b
)
2
+
4
is composite. Proposed by Serbia
number theory