Primitive Pythagorean 11-tuples (a, b, c, d, e, f, g, h, i, j, k) sorted.
1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 5, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 5, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 6, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 6, 1, 1, 1, 1, 1, 1, 1, 1, 4, 5, 7, 1, 1, 1, 1, 1, 1, 3, 3, 3, 4, 7, 1, 1, 1, 1, 1, 2, 2, 2, 4, 4, 7
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11-tuples such that k^2 = 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 k^2.
T. D. Noe, Plot of 1329 11-tuples
T. D. Noe, Table of 1329 11-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 + j^2; If[PerfectSquareQ[temp] && temp <= nMax^2 && GCD[a, b, c, d, e, f, g, h, i, j] == 1, cnt[[Sqrt[temp]]]++; AppendTo[t, {Sort[{a, b, c, d, e, f, g, h, i, j}], Sqrt[temp]}]], {a, nn, nn}, {b, a}, {c, b}, {d, c}, {e, d}, {f, e}, {g, f}, {h, g}, {i, h}, {j, i}], {nn, nMax}]; t
nonn,tabl
T. D. Noe, Aug 10 2017