Sets of 𝑛 squares of which any 𝑛-1 have their sum square

Lagrange, Jean

doi:10.1090/S0025-5718-1983-0717711-9

Sets of $n$ squares of which any $n-1$ have their sum square
HTML articles powered by AMS MathViewer

by Jean Lagrange PDF

Math. Comp. 41 (1983), 675-681 Request permission

Abstract:

A systematic method is given for calculating sets of n squares of which any $n - 1$ have their sum square. A particular method is developed for $n = 4$. Tables give the smallest solution for each $n \leqslant 8$ and other small solutions for $n \leqslant 5$.

References

Leonard Eugene Dickson, History of the theory of numbers. Vol. I: Divisibility and primality. , Chelsea Publishing Co., New York, 1966. MR 0245499

Angular Analysis Applied to Indeterminate Equations of the Second Degree

M. Lal and W. J. Blundon, Solutions of the Diophantine equations $x^{2}+y^{2}=l^{2},\,y^{2}+z^{2}=m^{2},\,z^{2}+x^{2}=n^{2}$. endx, Math. Comp. 20 (1966), 144–147. MR 186623, DOI 10.1090/S0025-5718-1966-0186623-4
John Leech, The rational cuboid revisited, Amer. Math. Monthly 84 (1977), no. 7, 518–533. MR 447106, DOI 10.2307/2320014
Masao Kishore, Odd integers $N$ with five distinct prime factors for which $2-10^{-12}<\sigma (N)/N<2+10^{-12}$, Math. Comp. 32 (1978), no. 141, 303–309. MR 485658, DOI 10.1090/S0025-5718-1978-0485658-X

Math. Quest. Educ. Times

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). MR 480309, DOI 10.24033/msmf.223

4

Math. Comp.

Math. Quest. Educ. Times