  We give a new characterization of generalized B\"uchi sequences (sequences
whose sequence of squares has constant second difference $(a)$, for some fixed
integer $a$) of length 3 over the integers and a strategy for attacking
B\"uchi's n Squares Problem. Known characterizations of integer B\"uchi
sequences of length 3 are actually characterizations over the rationals, plus
some divisibility criterions that keep integer sequences.
