On Arithmetic Partial Differential Equations
Pentti Haukkanen and Jorma K. Merikoski
School of Information Sciences
FI-33014 University of Tampere
Finland
Timo Tossavainen
School of Applied Educational Science and Teacher Education
University of Eastern Finland
P. O. Box 86
FI-57101 Savonlinna
Finland
Abstract:
Kovič, and implicitly Ufnarovski and Åhlander,
defined a notion of arithmetic partial derivative.
We generalize the definition for rational numbers and study several
arithmetic partial differential equations of the first and second
order. For some equations, we give a complete solution, and for
others, we extend previously known results. For example, we determine
under which conditions two consecutive partial derivations are
commutative.
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(Concerned with sequences
A000040
A003415.)
Received March 21 2016; revised versions received September 12 2016;
September 14 2016. Published in Journal of Integer Sequences,
October 11 2016.
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