Andrzej Tomski and Maciej Zakarczemny

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 23, 2017, Number 1, Pages 101—114

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## Details

### Authors and affiliations

Andrzej Tomski

*Institute of Mathematics, University of Silesia
Bankowa 14, 40-007 Katowice, Poland
*

Maciej Zakarczemny

*Institute of Mathematics, Cracow University of Technology
Warszawska 24, 31-155 Krakow, Poland
*

### Abstract

Let *f* be a natural-valued function defined on the Cartesian product of finitely many copies of ℕ (positive integers). Here we will discuss some modifications of the sieve of Eratosthenes in the sense that we cancel the divisors of all possible values of *f* in the points whose sum of coordinates is less or equal to *n*. By applying similar arguments to those used in the paper [J. Browkin, H-Q. Cao, *Modifications of the Eratosthenes sieve*, Colloq. Math. 135 (2014)], but also in the companion papers, we investigate new problems for the values of some polynomial functions or quadratic and cubic forms.

### Keywords

- Cancellation algorithms
- Primes in arithmetic progression
- Quadratic and cubic forms

### AMS Classification

- Primary 11A41
- Secondary 11N32, 11N36

### References

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## Cite this paper

Tomski, A., & Zakarczemny, M. (2017). On some cancellation algorithms. Notes on Number Theory and Discrete Mathematics, 23(1), 101-114.