Two triads of squares
Authors:
J. Lagrange and J. Leech
Journal:
Math. Comp. 46 (1986), 751758
MSC:
Primary 11D09
MathSciNet review:
829644
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
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, SpringerVerlag, New YorkBerlin,
1981. Problem Books in Mathematics. MR 656313
(83k:10002)
 [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
(47 #4913)
 [4]
John
Leech, The rational cuboid revisited, Amer. Math. Monthly
84 (1977), no. 7, 518–533. MR 0447106
(56 #5421)
 [5]
John
Leech, Two Diophantine birds with one stone, Bull. London
Math. Soc. 13 (1981), no. 6, 561–563. MR 634600
(82k:10017), http://dx.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
(15,645f), http://dx.doi.org/10.1090/S00029939195400602621
 [1]
 R. K. Guy, Unsolved Problems in Number Theory, SpringerVerlag, Berlin and New York, 1981. MR 656313 (83k:10002)
 [2]
 J. Lagrange, "Points du plan dont les distances mutuelles sont rationelles," Seminaire de Théorie des Nombres de Bordeaux, 19821983, Exposé no. 27, 10 pp. MR 750328
 [3]
 J. Leech, "The location of four squares in an arithmetic progression, with some applications," Computers in Number Theory (A. O. L. Atkin and B. J. Birch, eds.), Academic Press, London and New York, 1971, pp. 8398. MR 0316366 (47:4913)
 [4]
 J. Leech, "The rational cuboid revisited," Amer. Math. Monthly, v. 84, 1977, pp. 518533. MR 0447106 (56:5421)
 [5]
 J. Leech, "Two Diophantine birds with one stone," Bull. London Math. Soc., v. 13, 1981, pp. 561563. MR 634600 (82k:10017)
 [6]
 W. D. Peeples, "Elliptic curves and rational distance sets," Proc. Amer. Math. Soc., v. 5, 1954, pp. 2933. MR 0060262 (15:645f)
Similar Articles
Retrieve articles in Mathematics of Computation
with MSC:
11D09
Retrieve articles in all journals
with MSC:
11D09
Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198608296440
PII:
S 00255718(1986)08296440
Article copyright:
© Copyright 1986
American Mathematical Society
