MathDB
Problems
Contests
National and Regional Contests
Latvia Contests
Latvia BW TST
2020 Latvia Baltic Way TST
16
16
Part of
2020 Latvia Baltic Way TST
Problems
(1)
Sequence with gcd and lcm
Source: Latvian TST for Baltic Way 2020 P16
10/18/2020
Given sequence
{
a
n
}
\{a_n\}
{
a
n
}
satisfying:
a
n
+
1
=
l
c
m
(
a
n
,
a
n
−
1
)
gcd
(
a
n
,
a
n
−
1
)
a_{n+1} = \frac{ lcm(a_n,a_{n-1})}{\gcd(a_n, a_{n-1})}
a
n
+
1
=
g
cd
(
a
n
,
a
n
−
1
)
l
c
m
(
a
n
,
a
n
−
1
)
It is given that
a
209
=
209
a_{209} =209
a
209
=
209
and
a
361
=
361
a_{361} = 361
a
361
=
361
. Find all possible values of
a
2020
a_{2020}
a
2020
.
number theory
least common multiple
greatest common divisor