Sets of squares of which any have their sum square
Author:
Jean Lagrange
Journal:
Math. Comp. 41 (1983), 675681
MSC:
Primary 10B05; Secondary 10J05
MathSciNet review:
717711
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Abstract: A systematic method is given for calculating sets of n squares of which any have their sum square. A particular method is developed for . Tables give the smallest solution for each and other small solutions for .
 [1]
Leonard
Eugene Dickson, History of the theory of numbers. Vol. II:
Diophantine analysis, Chelsea Publishing Co., New York, 1966. MR 0245500
(39 #6807b)
 [2]
C. Gill, Angular Analysis Applied to Indeterminate Equations of the Second Degree, New York, 1848.
 [3]
M.
Lal and W.
J. Blundon, Math. Comp. 20 (1966), 144–147. MR 0186623
(32 #4082), http://dx.doi.org/10.1090/S00255718196601866234
 [4]
John
Leech, The rational cuboid revisited, Amer. Math. Monthly
84 (1977), no. 7, 518–533. MR 0447106
(56 #5421)
 [5]
Masao
Kishore, Addendum: “Odd integers 𝑁 with five distinct
prime factors for which
210⁻¹²<𝜎(𝑁)/𝑁<2+10⁻¹²”
(Math. Comp. 32 (1978), no. 141, 303–309), Math. Comp.
32 (1978), no. 141, loose microfiche suppl., 12. MR 0485659
(58 #5482b)
 [6]
A. Martin, "Find four square numbers such that the sum of every three of them shall be a square," Math. Quest. Educ. Times, v. 24, 1913, pp. 8182.
 [7]
JeanLouis
Nicolas, 6 nombres dont les sommes deux à deux sont des
carrés, Bull. Soc. Math. France Mém.
4950 (1977), 141–143 (French). Utilisation des
calculateurs en mathématiques pures (Conf., Limoges, 1975). MR 0480309
(58 #482)
 [8]
W. G. Spohn, UMT 4, "Table of integral cuboids and their generators," Math. Comp., v. 33, 1979, pp. 428429.
 [9]
S. Tebay, "Find four square numbers such that the sum of every three of them shall be a square," Math. Quest. Educ. Times, v. 68, 1898, pp. 103104.
 [1]
 L. E. Dickson, History of the Theory of Numbers, Vol. II: Diophantine Analysis, Carnegie Institute, Washington, 1920. Reprinted, Stechert, New York, 1934; Chelsea, New York, 1952, 1966. MR 0245500 (39:6807b)
 [2]
 C. Gill, Angular Analysis Applied to Indeterminate Equations of the Second Degree, New York, 1848.
 [3]
 M. Lal & W. J. Blundon, "Solutions of the Diophantine equations , , ," Math. Comp., v. 20, 1966, pp. 144147. MR 0186623 (32:4082)
 [4]
 J. Leech, "The rational cuboid revisited," Amer. Math. Monthly, v. 84, 1977, pp. 518533. MR 0447106 (56:5421)
 [5]
 J. Leech, UMT 12, "Five tables relating to rational cuboids," Math. Comp., v. 32, 1978, pp. 657659. MR 0485659 (58:5482b)
 [6]
 A. Martin, "Find four square numbers such that the sum of every three of them shall be a square," Math. Quest. Educ. Times, v. 24, 1913, pp. 8182.
 [7]
 J. L. Nicolas, "Six nombres dont les sommes deux à deux sont des carrés," Utilisation des calculateurs en mathématiques pures, Bull. Soc. Math. France Mem. No. 4950, 1977, pp. 141143. MR 0480309 (58:482)
 [8]
 W. G. Spohn, UMT 4, "Table of integral cuboids and their generators," Math. Comp., v. 33, 1979, pp. 428429.
 [9]
 S. Tebay, "Find four square numbers such that the sum of every three of them shall be a square," Math. Quest. Educ. Times, v. 68, 1898, pp. 103104.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198307177119
PII:
S 00255718(1983)07177119
Article copyright:
© Copyright 1983
American Mathematical Society
