A word is a finite sequence of letters from some alphabet. A word is 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 a word has the property that swapping any two adjacent letters makes the word repetitive, then all its letters are identical. (Note that one may swap two adjacent identical letters, leaving a word unchanged.)Romania (Dan Schwarz) modular arithmeticcombinatoricsEGMOEGMO 2012complex numbers