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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.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Sets in which $xy+k$ is always a square
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by Ezra Brown PDF
Math. Comp. 45 (1985), 613-620 Request permission


A ${P_k}$-set of size n is a set $\{ {x_1}, \ldots ,{x_n}\}$ of distinct positive integers such that ${x_i}{x_j} + k$ is a perfect square, whenever $i \ne j$; a ${P_k}$-set X can be extended if there exists $y \notin X$ such that $X \cup \{ y\}$ is still a ${P_k}$-set. The most famous result on ${P_k}$-sets is due to Baker and Davenport, who proved that the ${P_1}$-set 1, 3, 8, 120 cannot be extended. In this paper, we show, among other things, that if $k \equiv 2\;\pmod 4$, then there does not exist a ${P_k}$-set of size 4, and that the ${P_{ - 1}}$-set 1, 2, 5 cannot be extended.
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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Math. Comp. 45 (1985), 613-620
  • MSC: Primary 11D57
  • DOI:
  • MathSciNet review: 804949