MathDB
Problems
Contests
National and Regional Contests
Hong Kong Contests
Hong Kong National Olympiad
2009 Hong kong National Olympiad
1
1
Part of
2009 Hong kong National Olympiad
Problems
(1)
sequence
Source: 2009 HongKong mathematic Olympiad
2/11/2012
let
a
n
{a_{n}}
a
n
be a sequence of integers,
a
1
a_{1}
a
1
is odd,and for any positive integer
n
n
n
,we have
n
(
a
n
+
1
−
a
n
+
3
)
=
a
n
+
1
+
a
n
+
3
n(a_{n+1}-a_{n}+3)=a_{n+1}+a_{n}+3
n
(
a
n
+
1
−
a
n
+
3
)
=
a
n
+
1
+
a
n
+
3
,in addition,we have
2010
2010
2010
divides
a
2009
a_{2009}
a
2009
find the smallest
n
≥
2
n\ge\ 2
n
≥
2
,so that
2010
2010
2010
divides
a
n
a_{n}
a
n
algebra proposed
algebra