Integer squares with constant second difference

Author(s)

Duncan A. Buell, University of South Carolina - ColumbiaFollow

Document Type

Article

Abstract

The problem addressed is this: Do there exist nonconsecutive integers n₀, n₁, n₂, . . ., such that the second differences of the squares of the n_i are constant? Specifically, can that constant be equal to 2? A complete characterization of sequences of length four can be given. The question of whether or not sequences of length five exist is still open but the existence or nonexistence of such sequences can be described in a more algorithmic way than the simple statement of the problem.

Publication Info

Published in Mathematics of Computation, Volume 49, Issue 180, 1987, pages 635-644.

Rights

Buell, D.A. (1987). Integer squares with constant second difference. Mathematics of Computation, 49(180), 635-644.

First published in Mathematics of Computation in 1987, published by the American Mathematical Society.

Copyright ©1987 American Mathematical Society.