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
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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


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.


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

AMS Classification

  • Primary 11A41
  • Secondary 11N32, 11N36


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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.


Tomski, Andrzej, and Maciej Zakarczemny. ”On Some Cancellation Algorithms.” Notes on Number Theory and Discrete Mathematics 23, no. 1 (2017): 101-114.


Tomski, Andrzej, and Maciej Zakarczemny. “On Some Cancellation Algorithms.” Notes on Number Theory and Discrete Mathematics 23.1 (2017): 101-114. Print.

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