OFFSET
1,2
COMMENTS
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.
LINKS
Christopher Briggs, Python script for generating n-th term [warning: this program has errors]
Christopher Briggs, Y. Hirano, and H. Tsutsui, Positive Solutions to Some Systems of Diophantine Equations, Journal of Integer Sequences, 2016 Vol 19 #16.8.4.
Kinga Pósán and Szabolcs Tengely, SageMath code
Kinga Pósán, Table of solutions for n = 1..8
EXAMPLE
For n = 1, the only positive solution to x + y = xy is x = y = 2.
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).
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Christopher Briggs, Jul 20 2016
EXTENSIONS
Corrected by Kinga Pósán and Szabolcs Tengely, Mar 26 2022
STATUS
approved