

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



1, 2, 2, 4, 3, 6, 5, 10, 11, 17, 19, 36, 42, 70, 97, 155, 219, 351, 514, 815, 1228, 1918, 2937, 4614, 7111
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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

Table of n, a(n) for n=1..25.
Christopher Briggs, Python script for generating nth 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

Sequence in context: A341465 A304406 A053197 * A301768 A088145 A011754
Adjacent sequences: A275231 A275232 A275233 * A275235 A275236 A275237


KEYWORD

nonn,more


AUTHOR

Christopher Briggs, Jul 20 2016


EXTENSIONS

Corrected by Kinga Pósán and Szabolcs Tengely, Mar 26 2022


STATUS

approved



