MathDB
Problems
Contests
International Contests
IMO Longlists
1988 IMO Longlists
65
65
Part of
1988 IMO Longlists
Problems
(1)
GCD of the 1960-th and 1988-th terms of Fibonacci sequence
Source: IMO LongList 1988, South Korea 4, Problem 65 of ILL
11/3/2005
The Fibonacci sequence is defined by
a
n
+
1
=
a
n
+
a
n
−
1
,
n
≥
1
,
a
0
=
0
,
a
1
=
a
2
=
1.
a_{n+1} = a_n + a_{n-1}, n \geq 1, a_0 = 0, a_1 = a_2 = 1.
a
n
+
1
=
a
n
+
a
n
−
1
,
n
≥
1
,
a
0
=
0
,
a
1
=
a
2
=
1.
Find the greatest common divisor of the 1960-th and 1988-th terms of the Fibonacci sequence.
number theory
greatest common divisor
induction
algorithm
algebra unsolved
algebra