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On arithmetic partial differential equations. (English) Zbl 1353.11007
Summary: J. Kovič [J. Integer Seq. 15, No. 3, Article 12.3.8, 16 p. (2012; Zbl 1291.11009)], and implicitly V. Ufnarovski and B. Åhlander [J. Integer Seq. 6, No. 3, Art. 03.3.4, 24 p. (2003; Zbl 1142.11305)], 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.

MSC:
11A25 Arithmetic functions; related numbers; inversion formulas
11A51 Factorization; primality
Software:
OEIS
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