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%I #20 Nov 13 2012 23:58:45
%S 12,24,32,48,60,108,240,384,480,608,972,984,1020,2688
%N Numbers n for which the Hurwitz equation (x_1)^2 + (x_2)^2 + ... + (x_n)^2 = z * x_1 * x_2 * ... * x_n has solutions only for z = n.
%C Conjectured finite. Any further terms are greater than 10^8.
%H A. Hurwitz, <a href="http://www.archive.org/stream/archivdermathem16unkngoog#page/n207/mode/2up">Über eine Aufgabe der unbestimmten Analysis</a>, Archiv der Mathematik und Physik 11 (1907) pp. 185-196.
%H Norman P. Herzberg, <a href="http://projecteuclid.org/euclid.pjm/1102913235">On a problem of Hurwitz</a>, Pacific Journal of Mathematics 50 (1974), pp. 485-493.
%H Ioulia Baoulina and Florian Luca, <a href="http://ami.ektf.hu/uploads/papers/finalpdf/AMI_35_from11to19.pdf">On positive integers with a certain nondivisibility property</a>, Annales Mathematicae et Informaticae 35 (2008), pp. 11-19.
%K nonn,more
%O 1,1
%A _Charles R Greathouse IV_, Jul 26 2011
%E Definition corrected by _Max Alekseyev_, Nov 13 2012
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