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The problem addressed is this: Do there exist nonconsecutive integers n0, n1, n2, . . ., such that the second differences of the squares of the ni 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.


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.

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