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KoMaL A Problems
KoMaL A Problems 2018/2019
A. 730
A. 730
Part of
KoMaL A Problems 2018/2019
Problems
(1)
Fibonacci
Source: KöMaL A. 730
10/11/2018
Let
F
n
F_n
F
n
be the
n
n
n
th Fibonacci number (
F
1
=
F
2
=
1
F_1=F_2=1
F
1
=
F
2
=
1
and
F
n
+
1
=
F
n
+
F
n
−
1
F_{n+1}=F_n+F_{n-1}
F
n
+
1
=
F
n
+
F
n
−
1
). Construct infinitely many positive integers
n
n
n
such that
n
n
n
divides
F
F
n
F_{F_n}
F
F
n
but
n
n
n
does not divide
F
n
F_n
F
n
.
number theory