Tekuri Chalapathi, Shaik Sajana, and Dasari Bharathi
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 26, 2020, Number 1, Pages 59—69
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The interplay between algebraic structures and their elements have been the most
famous and productive area of the algebraic theory of numbers. Generally, the greatest
common divisor and least common multiple of any two positive integers are dependably
non-zero elements. In this paper, we introduce a new pair of elements, called classical pair in the ring Zn whose least common multiple is zero and concentrate the properties of these pairs. We establish a formula for determining the number of classical pairs in Zn for various values of n. Further, we present an algorithm for determining all these pairs in Zn.
- Greatest common divisor
- Least common multiple
- Euler-totient function
- Classical pairs
2010 Mathematics Subject Classification
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- Chalapathi, T., & Kiran Kumar, R. V. M. S. S. (2016). Graph structures of Euler totient numbers. Daffodil International Journal of Science and Technology. 11 (2), 19–29.
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- Buck, W. K. (2004). Cyclic Rings. Master Thesis, Eastern Illinois University.
- Sajana, S., & Bharathi, D. (2019). Number theoretic properties of the commutative ring Zn. Int. J. Res. Ind. Eng. 8 (1), 77–88.
Cite this paper
Chalapathi, T., Sajana, S., & Bharathi, D. (2020). Classical pairs in Zn. Notes on Number Theory and Discrete Mathematics, 26(1), 59-69, doi: 10.7546/nntdm.2020.26.1.59-69.