MathDB

5

Part of 2001 German National Olympiad

Problems(1)

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

Source: Germany 2001 p5

2/23/2020
The Fibonacci sequence is given by x1=x2=1x_1 = x_2 = 1 and xk+2=xk+1+xkx_{k+2} = x_{k+1} + x_k for each k∈Nk \in N. (a) Prove that there are Fibonacci numbes that end in a 99 in the decimal system. (b) Determine for which nn can a Fibonacci number end in nn 99-s in the decimal system.
fibonacci numbernumber theoryDigits