MathDB

Consider a sequence of words each consisting of two letters,

A

and

B

. The first word is "

A

" , while the second word is "

B

" . The

k

-th word is obtained from the (

k -2

)-nd by writing after it the (

k -1

)th one. (So the first few elements of the sequence are "

A

" , "

B

" ,"

AB

" , "

BAB

" , "

ABBAB

" . ) Does there exist in this sequence a "periodical" word, i.e. a word of the form

P P P ... P

, where

P

is a word , repeated at least once?
(Remark: For instance, the word

BABBBABB

is of the form

PP

, in which

P

is repeated exactly once . )
(A. Andjans, Riga)

Problem Statement