Question 62
A word is a finite sequence of letters from some alphabet. A word is called repetitive if it is a concatenation of at least two identical subwords (for example, $ababab$ and $abcabc$ are repetitive, but $ababa$ and $aabb$ are not). Prove that if every transposition of two adjacent letters transforms a word into a repetitive word, then all its letters are identical. A transposition of two identical adjacent letters, leaving the word unchanged, is also to be considered.