On Some Conjectures about Arithmetic Partial Differential Equations
Ram Krishna Pandey and Rohit Saxena
Department of Mathematics
Indian Institute of Technology Roorkee
Roorkee - 247667
In this paper, we study the arithmetic partial differential equations
x'p = axn
and x'p =
a. We solve a conjecture of Haukkanen, Merikoski, and
Tossavainen (HMT, in short) about the number of solutions (conjectured
to be finite) of the equation x'p =
and improve a theorem of HMT about finding the
solutions of the same equation. Furthermore, we also improve another
theorem of HMT about the solutions of the equation
x'p = a
and discuss one more conjecture of HMT about the number of
solutions of x'p = a.
Full version: pdf,
(Concerned with sequences
Received January 31 2017;
revised version received February 23 2017.
Published in Journal of Integer Sequences, March 26 2017.
Journal of Integer Sequences home page