Primitive Pythagorean 9-tuples (a, b, c, d, e, f, g, h, i) sorted.
1, 1, 1, 1, 1, 1, 1, 3, 4, 1, 1, 1, 1, 2, 2, 2, 3, 5, 1, 1, 2, 2, 2, 2, 3, 3, 6, 1, 1, 1, 1, 1, 2, 2, 6, 7, 1, 1, 1, 1, 2, 3, 4, 4, 7, 1, 1, 1, 2, 2, 2, 3, 5, 7, 1, 2, 2, 2, 3, 3, 3, 3, 7, 2, 2, 2, 2, 2, 2, 3, 4, 7, 1, 1, 1, 1, 1, 1, 3, 7, 8, 1, 1, 1, 1, 1, 3, 5, 5, 8
1
9-tuples such that i^2 = h^2 + g^2 + f^2 + e^2 + d^2 + c^2 + b^2 + a^2. There are only a finite number of cases that sum to a given i^2.
T. D. Noe, Plot of 1185 9-tuples
T. D. Noe, Table of 1185 9-tuples
(Mma) nMax = 5; cnt = Table[0, {nMax}]; t = {}; Do[Do[temp = a^2 + b^2 + c^2 + d^2 + e^2 + f^2 + g^2 + h^2; If[PerfectSquareQ[temp] && temp <= nMax^2 && GCD[a, b, c, d, e, f, g, h] == 1, cnt[[Sqrt[temp]]]++; AppendTo[t, {Sort[{a, b, c, d, e, f, g, h}], Sqrt[temp]}]], {a, nn, nn}, {b, a}, {c, b}, {d, c}, {e, d}, {f, e}, {g, f}, {h, g}], {nn, nMax}]; t
nonn,tabl
T. D. Noe, Aug 10 2017