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2015 Balkan MO Shortlist
N2
N2
Part of
2015 Balkan MO Shortlist
Problems
(1)
a_{n+4}=2a_{n+3}+a_{n+2}-2a_{n+1}-a_n, prove n^2 / a_n for infinite n
Source: Balkan BMO Shortlist 2015 N2
8/5/2019
Sequence
(
a
n
)
n
≥
0
(a_n)_{n\geq 0}
(
a
n
)
n
≥
0
is defined as
a
0
=
0
,
a
1
=
1
,
a
2
=
2
,
a
3
=
6
a_{0}=0, a_1=1, a_2=2, a_3=6
a
0
=
0
,
a
1
=
1
,
a
2
=
2
,
a
3
=
6
, and
a
n
+
4
=
2
a
n
+
3
+
a
n
+
2
−
2
a
n
+
1
−
a
n
,
n
≥
0
a_{n+4}=2a_{n+3}+a_{n+2}-2a_{n+1}-a_n, n\geq 0
a
n
+
4
=
2
a
n
+
3
+
a
n
+
2
−
2
a
n
+
1
−
a
n
,
n
≥
0
. Prove that
n
2
n^2
n
2
divides
a
n
a_n
a
n
for infinite
n
n
n
.(Romania)
recurrence relation
number theory with sequences
Sequence
divides
number theory
algebra