Sets of squares of which any have their sum square

Author:
Jean Lagrange

Journal:
Math. Comp. **41** (1983), 675-681

MSC:
Primary 10B05; Secondary 10J05

DOI:
https://doi.org/10.1090/S0025-5718-1983-0717711-9

MathSciNet review:
717711

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Abstract | References | Similar Articles | Additional Information

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. I: Divisibility and primality.*, Chelsea Publishing Co., New York, 1966. MR**0245499**

Leonard Eugene Dickson,*History of the theory of numbers. Vol. II: Diophantine analysis*, Chelsea Publishing Co., New York, 1966. MR**0245500**

Leonard Eugene Dickson,*History of the theory of numbers. Vol. III: Quadratic and higher forms.*, With a chapter on the class number by G. H. Cresse, Chelsea Publishing Co., New York, 1966. MR**0245501****[2]**C. Gill,*Angular Analysis Applied to Indeterminate Equations of the Second Degree*, New York, 1848.**[3]**M. Lal and W. J. Blundon,*Solutions of the Diophantine equations 𝑥²+𝑦²=𝑙²,𝑦²+𝑧²=𝑚²,𝑧²+𝑥²=𝑛². endx*, Math. Comp.**20**(1966), 144–147. MR**0186623**, https://doi.org/10.1090/S0025-5718-1966-0186623-4**[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]**Masao Kishore,*Odd integers 𝑁 with five distinct prime factors for which 2-10⁻¹²<𝜎(𝑁)/𝑁<2+10⁻¹²*, Math. Comp.**32**(1978), no. 141, 303–309. MR**0485658**, https://doi.org/10.1090/S0025-5718-1978-0485658-X

Masao Kishore,*Addendum: “Odd integers 𝑁 with five distinct prime factors for which 2-10⁻¹²<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**, https://doi.org/10.2307/2006281**[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. 81-82.**[7]**Jean-Louis Nicolas,*6 nombres dont les sommes deux à deux sont des carrés*, Bull. Soc. Math. France Mém.**49-50**(1977), 141–143 (French). Utilisation des calculateurs en mathématiques pures (Conf., Limoges, 1975). MR**0480309****[8]**W. G. Spohn, UMT**4**, "Table of integral cuboids and their generators,"*Math. Comp.*, v. 33, 1979, pp. 428-429.**[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. 103-104.

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DOI:
https://doi.org/10.1090/S0025-5718-1983-0717711-9

Article copyright:
© Copyright 1983
American Mathematical Society