MathDB

Prove that for each positive integer

k

there exists a number base

b

along with

k

triples of Fibonacci numbers

(F_u,F_v,F_w)

such that when they are written in base

b

, their concatenation is also a Fibonacci number written in base

b

. (Fibonacci numbers are defined by

F_1 = F_2 = 1

and

F_{n+2} = F_{n+1} + F_n

for all positive integers

n

.)
Proposed by Serbia

Problem Statement