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Integer Squares with Constant Second Difference

1987
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Mathematics of Computation
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The problem addressed is this: Do there exist nonconsecutive integers n0, nl,n2,. ■ ■, such that the second differences of the squares of the nt 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.

doi:10.2307/2008336
fatcat:cucc5hsfybhdfifr5e3brp3ojm