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%I #43 Mar 28 2022 08:13:55
%S 1,2,2,4,3,6,5,10,11,17,19,36,42,70,97,155,219,351,514,815,1228,1918,
%T 2937,4614,7111
%N Number of distinct positive solutions to the system of n Diophantine equations: x_1 + y_1 = x_2*y_2, x_2 + y_2 = x_3*y_3, ..., x_n + y_n = x_1*y_1.
%C In any solution, interchanging x_i and y_i for any i yields a new solution. So does a circular permutation of the solution. Two solutions are counted as distinct if one cannot be obtained from the other by these transformations.
%H Christopher Briggs, <a href="/A275234/a275234.txt">Python script for generating n-th term</a> [warning: this program has errors]
%H Christopher Briggs, Y. Hirano, and H. Tsutsui, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Briggs/briggs3.html">Positive Solutions to Some Systems of Diophantine Equations</a>, Journal of Integer Sequences, 2016 Vol 19 #16.8.4.
%H Kinga Pósán and Szabolcs Tengely, <a href="https://shrek.unideb.hu/~tengely/A275234.sage">SageMath code</a>
%H Kinga Pósán, <a href="https://shrek.unideb.hu/~tengely/A275234.pdf">Table of solutions for n = 1..8</a>
%e For n = 1, the only positive solution to x + y = xy is x = y = 2.
%e For n = 2, the only distinct (see comments) positive solutions to x_1 + y_1 = x_2*y_2, x_2 + y_2 = x_1 * y_1 are (x_1,y_1,x_2,y_2) = (2,2,2,2) and (1,5,2,3).
%K nonn,more
%O 1,2
%A _Christopher Briggs_, Jul 20 2016
%E Corrected by Kinga Pósán and _Szabolcs Tengely_, Mar 26 2022
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