Journal of Integer Sequences, Vol. 19 (2016), Article 16.8.4

Positive Solutions to Some Systems of Diophantine Equations


Christopher Briggs
Department of Mathematics
Embry-Riddle Aeronautical University
Prescott, AZ 86301
USA

Yasuyuki Hirano
School of Natural and Living Sciences Education
Naruto University of Education
772-0051 Tokushima Prefecture, Naruto
Japan

Hisaya Tsutsui
Department of Mathematics
Embry-Riddle Aeronautical University
Prescott, AZ 86301
USA

Abstract:

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 computing an arbitrary term of the sequence, and consider a graph-theoretic approach to computing the same.

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(Concerned with sequences A000010 A000041 A004526 A038548 A275234.)

Received July 29 2016; revised versions received September 23 2016; October 4 2016. Published in Journal of Integer Sequences, October 10 2016.

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