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Contests
National and Regional Contests
India Contests
India National Olympiad
1996 India National Olympiad
5
5
Part of
1996 India National Olympiad
Problems
(1)
Sequnece 1
Source: INMO 1996 Problem 5
10/6/2005
Define a sequence
(
a
n
)
n
≥
1
(a_n)_{n \geq 1}
(
a
n
)
n
≥
1
by
a
1
=
1
a_1 =1
a
1
=
1
and
a
2
=
2
a_2 =2
a
2
=
2
and
a
n
+
2
=
2
a
n
+
1
−
a
n
+
2
a_{n+2} = 2 a_{n+1} - a_n + 2
a
n
+
2
=
2
a
n
+
1
−
a
n
+
2
for
n
≥
1
n \geq 1
n
≥
1
. prove that for any
m
m
m
,
a
m
a
m
+
1
a_m a_{m+1}
a
m
a
m
+
1
is also a term in this sequence.
induction
number theory solved
number theory