MathDB

for which n can a Fibonacci number end in n 9-s in the decimal system.

Source: Germany 2001 p5

February 23, 2020

fibonacci numbernumber theoryDigits

Problem Statement

The Fibonacci sequence is given by

x_1 = x_2 = 1

and

x_{k+2} = x_{k+1} + x_k

for each

k \in N

. (a) Prove that there are Fibonacci numbes that end in a

9

in the decimal system. (b) Determine for which

n

can a Fibonacci number end in

n

9

-s in the decimal system.