Two triads of squares

Authors:
J. Lagrange and J. Leech

Journal:
Math. Comp. **46** (1986), 751-758

MSC:
Primary 11D09

DOI:
https://doi.org/10.1090/S0025-5718-1986-0829644-0

MathSciNet review:
829644

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Abstract: The thirteen points (0,0), , , , , will be at integer distances from one another if the two triads , , , , , are such that the nine sums are all perfect squares. Infinite families of solutions are derived from solutions of , where , etc. Additional numerical examples are given. Two solutions are given in which one of the triads is extended to a tetrad.

**[1]**Richard K. Guy,*Unsolved problems in number theory*, Unsolved Problems in Intuitive Mathematics, vol. 1, Springer-Verlag, New York-Berlin, 1981. Problem Books in Mathematics. MR**656313****[2]**Jean Lagrange,*Points du plan dont les distances mutuelles sont rationnelles*, Seminar on number theory, 1982–1983 (Talence, 1982/1983) Univ. Bordeaux I, Talence, 1983, pp. Exp. No. 27, 10 (French). MR**750328****[3]**John Leech,*The location of four squares in an arithmetic progression, with some applications*, Computers in number theory (Proc. Sci. Res. Council Atlas Sympos. No. 2, Oxford, 1969) Academic Press, London, 1971, pp. 83–98. MR**0316366****[4]**John Leech,*The rational cuboid revisited*, Amer. Math. Monthly**84**(1977), no. 7, 518–533. MR**0447106**, https://doi.org/10.2307/2320014**[5]**John Leech,*Two Diophantine birds with one stone*, Bull. London Math. Soc.**13**(1981), no. 6, 561–563. MR**634600**, https://doi.org/10.1112/blms/13.6.561**[6]**W. D. Peeples Jr.,*Elliptic curves and rational distance sets*, Proc. Amer. Math. Soc.**5**(1954), 29–33. MR**0060262**, https://doi.org/10.1090/S0002-9939-1954-0060262-1

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DOI:
https://doi.org/10.1090/S0025-5718-1986-0829644-0

Article copyright:
© Copyright 1986
American Mathematical Society