We present a generalization of a known fact from combinatorics on words
related to periodicity into quasiperiodicity. A string is called periodic if it
has a period which is at most half of its length. A string w is called
quasiperiodic if it has a non-trivial cover, that is, there exists a string c
that is shorter than w and such that every position in w is inside one of
the occurrences of c in w. It is a folklore fact that two strings that
differ at exactly one position cannot be both periodic. Here we prove a more
general fact that two strings that differ at exactly one position cannot be
both quasiperiodic. Along the way we obtain new insights into combinatorics of
quasiperiodicities.Comment: 6 pages, 3 figure
