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National and Regional Contests
Brazil Contests
Brazil National Olympiad
2004 Brazil National Olympiad
3
3
Part of
2004 Brazil National Olympiad
Problems
(1)
Integer sequence
Source: Brazilian M.O. 2004
10/17/2004
Let
x
1
,
x
2
,
.
.
.
,
x
2004
x_1, x_2, ..., x_{2004}
x
1
,
x
2
,
...
,
x
2004
be a sequence of integer numbers such that
x
k
+
3
=
x
k
+
2
+
x
k
x
k
+
1
x_{k+3}=x_{k+2}+x_{k}x_{k+1}
x
k
+
3
=
x
k
+
2
+
x
k
x
k
+
1
,
∀
1
≤
k
≤
2001
\forall 1 \le k \le 2001
∀1
≤
k
≤
2001
. Is it possible that more than half of the elements are negative?
induction
algebra unsolved
algebra