Squares in quadratic progression

Pinch, R. G. E.

doi:10.1090/S0025-5718-1993-1181330-X

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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Squares in quadratic progression
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by R. G. E. Pinch PDF

Math. Comp. 60 (1993), 841-845 Request permission

Abstract:

The sequence of consecutive integer squares has constant second difference 2. We list every such sequence of squares containing a term less than ${1000^2}$.

References

D. Allison, On square values of quadratics, Math. Proc. Cambridge Philos. Soc. 99 (1986), no. 3, 381–383. MR 830351, DOI 10.1017/S030500410006432X
Duncan A. Buell, Integer squares with constant second difference, Math. Comp. 49 (1987), no. 180, 635–644. MR 906196, DOI 10.1090/S0025-5718-1987-0906196-9
R. G. E. Pinch, Simultaneous Pellian equations, Math. Proc. Cambridge Philos. Soc. 103 (1988), no. 1, 35–46. MR 913448, DOI 10.1017/S0305004100064598

Square values of quadratic polynomials