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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

Two triads of squares


Authors: J. Lagrange and J. Leech
Journal: Math. Comp. 46 (1986), 751-758
MSC: Primary 11D09
MathSciNet review: 829644
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Abstract: The thirteen points (0,0), $ ( \pm {a_i},0)$, $ i = 1,2,3$, $ (0, \pm {b_j})$, $ j = 1,2,3$, will be at integer distances from one another if the two triads $ a_1^2$, $ a_2^2$, $ a_3^2$, $ b_1^2$, $ b_2^2$, $ b_3^2$ are such that the nine sums $ a_i^2 + b_j^2$ are all perfect squares. Infinite families of solutions are derived from solutions of $ {\{ m,n\} ^2} = \{ p,q\} \{ r,s\} $, where $ \{ m,n\} = ({m^2} - {n^2})/2mn$, etc. Additional numerical examples are given. Two solutions are given in which one of the triads is extended to a tetrad.


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DOI: http://dx.doi.org/10.1090/S0025-5718-1986-0829644-0
PII: S 0025-5718(1986)0829644-0
Article copyright: © Copyright 1986 American Mathematical Society