MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
Akdeniz University MO
1997 Akdeniz University MO
3
sequence
sequence
Source:
January 30, 2016
equation
Sequence
Sequences
number theory
Problem Statement
(
x
n
)
(x_n)
(
x
n
)
be a sequence with
x
1
=
0
x_1=0
x
1
=
0
,
x
n
+
1
=
5
x
n
+
24
x
n
2
+
1
x_{n+1}=5x_n + \sqrt{24x_n^2+1}
x
n
+
1
=
5
x
n
+
24
x
n
2
+
1
. Prove that for
k
≥
2
k \geq 2
k
≥
2
x
k
x_k
x
k
is a natural number.
Back to Problems
View on AoPS