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2023 Indonesia MO
5
5
Part of
2023 Indonesia MO
Problems
(1)
Another NT with GCD and LCM
Source: INAMO 2023 P5 (OSN 2023)
8/30/2023
Let
a
a
a
and
b
b
b
be positive integers such that
gcd
(
a
,
b
)
+
lcm
(
a
,
b
)
\text{gcd}(a, b) + \text{lcm}(a, b)
gcd
(
a
,
b
)
+
lcm
(
a
,
b
)
is a multiple of
a
+
1
a+1
a
+
1
. If
b
≤
a
b \le a
b
≤
a
, show that
b
b
b
is a perfect square.
number theory
greatest common divisor
least common multiple
Indonesia
Indonesia MO