MathDB
Problems
Contests
National and Regional Contests
Netherlands Contests
Dutch BxMO/EGMO TST
2019 Dutch BxMO TST
4
4
Part of
2019 Dutch BxMO TST
Problems
(1)
a_n = gcd(a_{n+k}, a_{n+k+1}) for all n, sequence a_n
Source: Dutch BxMO TST 2019 p4
1/10/2020
Do there exist a positive integer
k
k
k
and a non-constant sequence
a
1
,
a
2
,
a
3
,
.
.
.
a_1, a_2, a_3, ...
a
1
,
a
2
,
a
3
,
...
of positive integers such that
a
n
=
g
c
d
(
a
n
+
k
,
a
n
+
k
+
1
)
a_n = gcd(a_{n+k}, a_{n+k+1})
a
n
=
g
c
d
(
a
n
+
k
,
a
n
+
k
+
1
)
for all positive integers
n
n
n
?
GCD
number theory
greatest common divisor
Sequence