Primitive Pythagorean 10-tuples (a, b, c, d, e, f, g, h, i, j) sorted.
1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 3, 5, 1, 1, 1, 1, 1, 1, 1, 2, 5, 6, 1, 1, 1, 1, 1, 2, 3, 3, 3, 6, 1, 1, 1, 1, 2, 2, 2, 2, 4, 6, 1, 1, 1, 1, 1, 1, 3, 3, 5, 7, 1, 1, 1, 1, 3, 3, 3, 3, 3, 7, 1, 1, 1, 2, 2, 2, 3, 3, 4, 7, 1, 1, 1, 1, 1, 3, 3, 4, 5, 8
1
10-tuples such that j^2 = 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 j^2.
T. D. Noe, Plot of 1236 10-tuples
T. D. Noe, Table of 1236 10-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 + i^2; If[PerfectSquareQ[temp] && temp <= nMax^2 && GCD[a, b, c, d, e, f, g, h, i] == 1, cnt[[Sqrt[temp]]]++; AppendTo[t, {Sort[{a, b, c, d, e, f, g, h, i}], Sqrt[temp]}]], {a, nn, nn}, {b, a}, {c, b}, {d, c}, {e, d}, {f, e}, {g, f}, {h, g}, {i, h}], {nn, nMax}]; t
nonn,tabl
T. D. Noe, Aug 10 2017