MathDB
Problems
Contests
International Contests
Baltic Way
2022 Baltic Way
18
18
Part of
2022 Baltic Way
Problems
(1)
GCD relation
Source: Baltic Way 2022, Problem 18
11/12/2022
Find all pairs
(
a
,
b
)
(a, b)
(
a
,
b
)
of positive integers such that
a
≤
b
a \le b
a
≤
b
and
gcd
(
x
,
a
)
gcd
(
x
,
b
)
=
gcd
(
x
,
20
)
gcd
(
x
,
22
)
\gcd(x, a) \gcd(x, b) = \gcd(x, 20) \gcd(x, 22)
g
cd
(
x
,
a
)
g
cd
(
x
,
b
)
=
g
cd
(
x
,
20
)
g
cd
(
x
,
22
)
holds for every positive integer
x
x
x
.
number theory
greatest common divisor