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Positive Solutions to Some Systems of Diophantine Equations
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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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