On Some Conjectures about Arithmetic Partial Differential Equations
نویسندگان
چکیده
In this paper, we study the arithmetic partial differential equations x′p = ax n 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 = ax n 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.
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