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Germany Contests
German National Olympiad
2012 German National Olympiad
1
1
Part of
2012 German National Olympiad
Problems
(1)
Standard sequence contains infinitely many composite integers
Source: Germany 2012 - Problem 1
12/5/2022
Define a sequence
(
a
n
)
(a_n)
(
a
n
)
by
a
0
=
−
4
,
a
1
=
−
7
a_0 =-4 , a_1 =-7
a
0
=
−
4
,
a
1
=
−
7
and
a
n
+
2
=
5
a
n
+
1
−
6
a
n
a_{n+2}= 5a_{n+1} -6a_n
a
n
+
2
=
5
a
n
+
1
−
6
a
n
for
n
≥
0.
n\geq 0.
n
≥
0.
Prove that there are infinitely many positive integers
n
n
n
such that
a
n
a_n
a
n
is composite.
number theory
Sequence
recursive
Composite