Let  be a geometric progression of natural numbers whose quotient has exactly k distinct prime divisors. In this note, we show that the  differences of the sequence  constitute an arithmetic progression. Moreover, we show that there exists a polynomial p of degree k such that  for each

number of divisors, geometric progression, interpolation polynomial.

Received: January 28, 2024; Accepted: February 16, 2024; Published: February 29, 2024

How to cite this article: Slobodan Filipovski, On the number of divisors of the terms of a geometric progression, Far East Journal of Mathematical Education 26(1) (2024), 29-33. http://dx.doi.org/10.17654/0973563124004

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] D. M. Burton, Elementary Number Theory, McGraw-Hill, New York, 2012.
[2] M. Zabrocki, Differences of Sequences, York University.