English

A characterization of B\"uchi's integer sequences of length 3

Number Theory 2010-11-11 v1

Abstract

We give a new characterization of generalized B\"uchi sequences (sequences whose sequence of squares has constant second difference (a)(a), for some fixed integer aa) 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.

Keywords

Cite

@article{arxiv.1011.2251,
  title  = {A characterization of B\"uchi's integer sequences of length 3},
  author = {Pablo Saéz and Xavier Vidaux},
  journal= {arXiv preprint arXiv:1011.2251},
  year   = {2010}
}
R2 v1 2026-06-21T16:41:32.111Z