MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
Akdeniz University MO
1996 Akdeniz University MO
2
fibonacci sequence
fibonacci sequence
Source:
January 29, 2016
Fibonacci
Sequence
number theory
Problem Statement
Let
u
1
=
1
,
u
2
=
1
u_1=1,u_2=1
u
1
=
1
,
u
2
=
1
and for all
k
≥
1
k \geq 1
k
≥
1
's
u
k
+
2
=
u
k
+
1
+
u
k
u_{k+2}=u_{k+1}+u_{k}
u
k
+
2
=
u
k
+
1
+
u
k
Prove that for all
m
≥
1
m \geq 1
m
≥
1
's
5
5
5
divides
u
5
m
u_{5m}
u
5
m
Back to Problems
View on AoPS