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Problems
Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
2007 National Olympiad First Round
19
19
Part of
2007 National Olympiad First Round
Problems
(1)
Turkey NMO 2007 1st Round - P19 (Algebra)
Source:
10/4/2012
If
x
1
=
5
,
x
2
=
401
x_1=5, x_2=401
x
1
=
5
,
x
2
=
401
, and
x
n
=
x
n
−
2
−
1
x
n
−
1
x_n=x_{n-2}-\frac 1{x_{n-1}}
x
n
=
x
n
−
2
−
x
n
−
1
1
for every
3
≤
n
≤
m
3\leq n \leq m
3
≤
n
≤
m
, what is the largest value of
m
m
m
?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
406
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
2005
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
2006
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
2007
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
None of the above
<span class='latex-bold'>(A)</span>\ 406 \qquad<span class='latex-bold'>(B)</span>\ 2005 \qquad<span class='latex-bold'>(C)</span>\ 2006 \qquad<span class='latex-bold'>(D)</span>\ 2007 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the above}
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
406
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
2005
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
2006
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
2007
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
None of the above
AMC
AIME
AIME II