A characterization of Büchi's integer sequences of length 3

Abstract

We give a new characterization of generalized Büchi 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 Büchi's n Squares Problem. Known characterizations of integer Büchi sequences of length 3 are actually characterizations over the rationals, plus some divisibility criterions that keep integer sequences.