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A309810 Orders of Parker rings. 0


%S 2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,

%T 28,30,31,32,33,34,36,38,39,40,42,43,44,46,47,48,49,51,52,56,57,60,62,

%U 64,66,67,68,69,72,75,76,78,80,84,86,88,92,93,94,96,100,102,104,112,114

%N Orders of Parker rings.

%C A field or ring is called "Parker" if no 3 X 3 magic square of 9 distinct squared elements can be formed. Conjecture: the sequence is complete.

%C Example: the fact that p=31 is listed is taken to mean one cannot construct a 3 X 3 magic square of distinct squared elements of the ring of order 31.

%H Onno M. Cain, <a href="https://github.com/onnomc/parker-ring-search">parker-ring-search SageMath code</a>, Apr 24, 2019.

%H Onno M. Cain, <a href="https://arxiv.org/abs/1908.03236">Gaussian Integers, Rings, Finite Fields and the Magic Square of Squares</a>, arXiv:1908.03236 [math.RA], 2019.

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

%Y Cf. A308838 (for finite field).

%K nonn

%O 1,1

%A _Michel Marcus_, Aug 18 2019

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Last modified January 29 14:07 EST 2020. Contains 331338 sequences. (Running on oeis4.)