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The Anti-Parker Square, read by rows.
1

%I #12 Dec 20 2024 02:37:12

%S 8288641,16492609,4515625,5992609,9765625,13538641,15015625,3038641,

%T 11242609

%N The Anti-Parker Square, read by rows.

%C This square has been discovered by Ayliean MacDonald (see links) while attempting to create a magic square of squares.

%C It's an example of a 3 X 3 square where all rows, columns and diagonals sum to the same number (in this case 29296875), but only the entries in the diagonals are squares.

%C The Parker Square (A364264) was an attempt (which failed in a different way) to solve the same problem.

%H Brady Haran and Ayliean MacDonald, <a href="https://www.youtube.com/watch?v=uz9jOIdhzs0">The Anti-Parker Square</a>, YouTube Numberphile video, 2024.

%H Brady Haran and Matt Parker, <a href="https://www.youtube.com/watch?v=aOT_bG-vWyg">The Parker Square</a>, YouTube Numberphile video, 2016.

%e The Anti-Parker Square is:

%e [ 8288641 16492609 4515625 ]

%e [ 5992609 9765625 13538641 ]

%e [ 15015625 3038641 11242609 ]

%e Or equivalently:

%e [ 2879^2 16492609 2125^2 ]

%e [ 5992609 3125^2 13538641 ]

%e [ 3875^2 3038641 3353^2 ]

%Y Cf. A364264.

%K nonn,tabf,fini,full

%O 1,1

%A _Paolo Xausa_, Dec 17 2024