MathDB

A finite sequence of natural numbers

a_1, a_2, \dots, a_n

is given. A sub-sequence

a_{k+1}, a_{k+2}, \dots, a_l

will be called a repetition if there exists a natural number

p\leq \frac{l-k}2

such that

a_i=a_{i+p}

for

k+1\leq i\leq l-p

, but

a_i\neq a_{i+p}

for

i=k

(if

k>0

) and

i=l-p+1

(if

l<n

).
Show that the sequence contains less than

n

repetitions.

Problem Statement