MathDB
Problems
Contests
National and Regional Contests
China Contests
National High School Mathematics League
1988 National High School Mathematics League
1
Recurrence Sequence
Recurrence Sequence
Source: 1988 National High School Mathematics League, Exam Two, Problem 1
February 25, 2020
Problem Statement
Define sequence
(
a
n
)
:
a
1
=
1
,
a
2
=
2
,
a
n
+
2
=
{
5
a
n
+
1
−
3
a
n
,
if
a
n
⋅
a
n
+
1
is even
a
n
+
1
−
a
n
,
if
a
n
⋅
a
n
+
1
is odd
(a_n):a_1=1,a_2=2,a_{n+2}=\begin{cases} 5a_{n+1}-3a_n,\text{if }a_n\cdot a_{n+1}\text{ is even}\\ a_{n+1}-a_n,\text{if }a_n\cdot a_{n+1}\text{ is odd} \end{cases}
(
a
n
)
:
a
1
=
1
,
a
2
=
2
,
a
n
+
2
=
{
5
a
n
+
1
−
3
a
n
,
if
a
n
⋅
a
n
+
1
is even
a
n
+
1
−
a
n
,
if
a
n
⋅
a
n
+
1
is odd
Prove that for all
n
∈
Z
+
n\in\mathbb{Z}_+
n
∈
Z
+
,
a
n
≠
0
a_n\neq0
a
n
=
0
.
Back to Problems
View on AoPS