Sets in which is always a square

Author:
Ezra Brown

Journal:
Math. Comp. **45** (1985), 613-620

MSC:
Primary 11D57

MathSciNet review:
804949

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Abstract: A -set of size *n* is a set of distinct positive integers such that is a perfect square, whenever ; a -set *X* can be extended if there exists such that is still a -set. The most famous result on -sets is due to Baker and Davenport, who proved that the -set 1, 3, 8, 120 cannot be extended. In this paper, we show, among other things, that if , then there does not exist a -set of size 4, and that the -set 1, 2, 5 cannot be extended.

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DOI:
https://doi.org/10.1090/S0025-5718-1985-0804949-7

Article copyright:
© Copyright 1985
American Mathematical Society