MathDB

A sequence

x_0=A

and

x_1=B

and

x_{n+2}=x_{n+1} +x_n

is called a Fibonacci type sequence. Call a number

C

a repeated value if

x_t=x_s=c

for

t

different from

s

. Prove one can choose

A

and

B

to have as many repeated value as one likes but never infinite.

Problem Statement