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GCD of the 1960-th and 1988-th terms of Fibonacci sequence

Source: IMO LongList 1988, South Korea 4, Problem 65 of ILL

November 3, 2005
number theorygreatest common divisorinductionalgorithmalgebra unsolvedalgebra

Problem Statement

The Fibonacci sequence is defined by an+1=an+an−1,n≥1,a0=0,a1=a2=1. a_{n+1} = a_n + a_{n-1}, n \geq 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.
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