On some cancellation algorithms

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
Full paper (PDF, 224 Kb)

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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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