Integer squares with constant second difference

Author:
Duncan A. Buell

Journal:
Math. Comp. **49** (1987), 635-644

MSC:
Primary 11Y55; Secondary 11B83

MathSciNet review:
906196

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

**[1]**D. Allison,*On square values of quadratics*, Math. Proc. Cambridge Philos. Soc.**99**(1986), no. 3, 381–383. MR**830351**, 10.1017/S030500410006432X**[2]**E. J. Barbeau,*Numbers differing from consecutive squares by squares*, Canad. Math. Bull.**28**(1985), no. 3, 337–342. MR**790955**, 10.4153/CMB-1985-040-9**[3]**Douglas C. Hensley, "Sequences of squares with second difference of 2 and a problem of logic," unpublished.**[4]**Leonard Lipschitz, personal correspondence.

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DOI:
https://doi.org/10.1090/S0025-5718-1987-0906196-9

Article copyright:
© Copyright 1987
American Mathematical Society