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A358445 Euler's 4 X 4 magic square of squares.

%I A358445 #52 Feb 12 2024 08:39:21
%S A358445 4624,841,1681,1369,289,961,6241,1024,3481,784,529,3721,121,5929,64,
%T A358445 2401
%N A358445 Euler's 4 X 4 magic square of squares.
%C A358445 This is the first known magic square of squares; Euler sent it to Lagrange in 1770.
%C A358445 The magic sum is 8515.
%H A358445 Paul Pierrat, François Thiriet, and Paul Zimmermann, <a href="https://web.archive.org/web/20210921105123/https://members.loria.fr/PZimmermann/papers/squares.pdf">Magic Squares of Squares</a>.
%H A358445 Philippe Michaud-Rodgers, <a href="https://warwick.ac.uk/fac/sci/maths/people/staff/michaud/magisquarestalk.pdf">Magic Squares of Squares</a>.
%H A358445 Ivars Peterson, <a href="https://www.sciencenews.org/article/magic-squares-squares">Magic Squares of Squares</a>.
%e A358445 The magic square is:
%e A358445  [ 4624  841 1681 1369 ]
%e A358445  [  289  961 6241 1024 ]
%e A358445  [ 3481  784  529 3721 ]
%e A358445  [  121 5929   64 2401 ]
%e A358445 Equivalently:
%e A358445  [ 68^2 29^2 41^2 37^2 ]
%e A358445  [ 17^2 31^2 79^2 32^2 ]
%e A358445  [ 59^2 28^2 23^2 61^2 ]
%e A358445  [ 11^2 77^2  8^2 49^2 ]
%Y A358445 Cf. A271580: magic sums of 4 X 4 magic squares composed of squares.
%K A358445 nonn,fini,full
%O A358445 1,1
%A A358445 _Robert C. Lyons_, Dec 30 2022