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2023 Balkan MO Shortlist
N2
3 coprime numbers satisfying gcd condition
3 coprime numbers satisfying gcd condition
Source: BMO SL 2023 N2
May 3, 2024
number theory
Problem Statement
Find all positive integers, such that there exist positive integers
a
,
b
,
c
a, b, c
a
,
b
,
c
, satisfying
gcd
(
a
,
b
,
c
)
=
1
\gcd(a, b, c)=1
g
cd
(
a
,
b
,
c
)
=
1
and
n
=
gcd
(
a
b
+
c
,
a
c
−
b
)
=
a
+
b
+
c
n=\gcd(ab+c, ac-b)=a+b+c
n
=
g
cd
(
ab
+
c
,
a
c
−
b
)
=
a
+
b
+
c
.
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