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Integer Squares With Constant Second Difference, Duncan A. Buell
Integer Squares With Constant Second Difference, Duncan A. Buell
Faculty Publications
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.
Sequentially Compact, Franklin-Rajagopalan Spaces, Peter J. Nyikos, J. E. Vaughan
Sequentially Compact, Franklin-Rajagopalan Spaces, Peter J. Nyikos, J. E. Vaughan
Faculty Publications
No abstract provided.
Class Groups Of Quadratic Fields Ii, Duncan A. Buell
Class Groups Of Quadratic Fields Ii, Duncan A. Buell
Faculty Publications
A computation has been made of the noncyclic class groups of imaginary quadratic fields Q(√-D) for even and odd discriminants - D from 0 to - 25000000. Among the results are that 95% of the class groups are cyclic, and that -11203620 and -18397407 are the first discriminants of imaginary quadratic fields for which the class group has rank three in the 5-Sylow subgroup. The latter was known to be of rank three; this computation demonstrates that it is the first odd discriminant of 5-rank three or more.