DIVISIBILITY RULES FOR 13: MATHEMATICAL PROOFS AND PRACTICAL ALGORITHMS

Authors

  • Mahamadiyeva Aziza Sherali qizi Teacher of Termez State Pedagogical Institute
  • Tursinova Sokhiba Ravshon qizi, Khojakulova Nozima Abduhamid qizi Students of Termez State Pedagogical Institute

Keywords:

Divisibility rules, divisibility by 13, mathematical proofs, practical algorithms, number theory, modular arithmetic, osculation method.

Abstract

The integer 13, being a prime number, presents unique challenges in mental arithmetic and computational efficiency compared to composite divisors. This article explores the mathematical foundations of divisibility rules for 13, focusing on the method of osculation and modular congruences. We provide rigorous proofs for common algorithms and evaluate their practical application in number theory and pedagogy.

References

G.H. Hardy and E.M. Wright, "An Introduction to the Theory of Numbers". Oxford University Press.

D.M. Burton, "Elementary Number Theory". McGraw-Hill Education.

T.H. Cormen, et al., "Introduction to Algorithms". MIT Press.

M. Mirzaahmedov, Sh. Ismoilov, A. Amanov, "Matematika: Umumiy o'rta ta'lim maktablarining 6-sinfi uchun darslik".

A.S. Vorobyov, "Priznaki delimosti" (Bo'linish alomatlari). Moskva, Nauka.

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Published

2026-05-12

How to Cite

Mahamadiyeva Aziza Sherali qizi, & Tursinova Sokhiba Ravshon qizi, Khojakulova Nozima Abduhamid qizi. (2026). DIVISIBILITY RULES FOR 13: MATHEMATICAL PROOFS AND PRACTICAL ALGORITHMS. Ethiopian International Multidisciplinary Research Conferences, 3(2), 108–109. Retrieved from https://eijmr.org/conferences/index.php/eimrc/article/view/2234

Issue

Vol. 3 No. 2 (2026): Ethiopian International Multidisciplinary Research Conferences

Section

Articles

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