Positive Solutions to Some Systems of Diophantine Equations

Christopher Briggs, Yasuyuki Hirano, Hisaya Tsutsui
2016 Journal of Integer Sequences   unpublished
We consider a sequence defined by the number of positive solutions to a sequence of systems of Diophantine equations. We derive some bounds on the solutions to demonstrate that the terms of the sequence are finite. We develop an algorithm for 1 computing an arbitrary term of the sequence, and consider a graph-theoretic approach to computing the same.