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A275234 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. 1

%I

%S 1,2,2,3,3,5,4,7,7,12,12,21,22,37,47,72,93,145,198,303,427,637,917,

%T 1383,2008

%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 gotten from the other by these transformations.

%H Christopher Briggs, <a href="/A275234/a275234.txt">Python script for generating nth term</a>

%H Christopher Briggs, Y. Hirano, 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.

%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_2 = 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) or (1,5,2,3).

%K nonn,more

%O 1,2

%A _Christopher Briggs_, Jul 20 2016

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Last modified January 25 05:34 EST 2022. Contains 350565 sequences. (Running on oeis4.)