On the Solution of the Equation
n = ak + bpk
by Means of an Iterative Method
Juan Luis Varona
Departamento de Matemáticas y Computación
Universidad de La Rioja
For fixed positive integers n
, we study the solution of the equation
denotes the k
th prime number, by means
of the iterative method
which converges to the solution of the equation, if it exists.
We also analyze the equation
for fixed integer values
and its solution by means of a corresponding iterative method.
The case a
>0 is somewhat similar to the case a
while for a
<0 the convergence and usefulness of the method
are less satisfactory.
The paper also includes a study of the dynamics of the iterative methods.
Full version: pdf,
(Concerned with sequences
Received March 21 2021; revised versions received March 23 2021; November 16 2021; November 21 2021.
Published in Journal of Integer Sequences,
November 27 2021.
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