  Entringer, Jackson, and Schatz conjectured in 1974 that every infinite
cubefree binary word contains arbitrarily long squares. In this paper we show
this conjecture is false: there exist infinite cubefree binary words avoiding
all squares xx with |x| >= 4, and the number 4 is best possible. However, the
Entringer-Jackson-Schatz conjecture is true if "cubefree" is replaced with
"overlap-free".
