MathDB
Problems
Contests
National and Regional Contests
Brazil Contests
Brazil National Olympiad
2004 Brazil National Olympiad
5
5
Part of
2004 Brazil National Olympiad
Problems
(1)
Prove that all the terms are integer
Source: Brazilian M.O. 2004
10/18/2004
Consider the sequence
(
a
n
)
n
∈
N
(a_n)_{n\in \mathbb{N}}
(
a
n
)
n
∈
N
with
a
0
=
a
1
=
a
2
=
a
3
=
1
a_0=a_1=a_2=a_3=1
a
0
=
a
1
=
a
2
=
a
3
=
1
and
a
n
a
n
−
4
=
a
n
−
1
a
n
−
3
+
a
n
−
2
2
a_na_{n-4}=a_{n-1}a_{n-3} + a^2_{n-2}
a
n
a
n
−
4
=
a
n
−
1
a
n
−
3
+
a
n
−
2
2
. Prove that all the terms of this sequence are integer numbers.
induction
modular arithmetic
algebra
polynomial
number theory unsolved
number theory