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DISTRIBUTION OF DIVISORS OF AN INTEGER IN A TRIANGLE INTEGER SEQUENCE
Keywords:
integer sequence, divisor, distribution, probability, randomizationDOI:
https://doi.org/10.17654/0972555524011Abstract
An integer sequence is defined to study the distribution of the divisors of an odd integer $N$, theorems are proven to count the terms owning a divisor of $N$ in the sequence, and distributions of those terms are discovered. A subset having a higher probability of picking randomly an element owning a divisor of $N$ is found by comparing different subsets constructed from the integer sequence.
Received: January 18, 2024
Accepted: February 28, 2024
References
Titu Andreescu and Dorin Andrica, Number Theory Structures, Examples, and Problems, Birkhäuser, 2009.
David M. Burton, Elementary Number Theory, 7th ed., McGraw-Hill, 2010.
K. H. Rosen, Elementary Number Theory and its Applications, 6th ed., Addison-Wesley, 2011.
Ford Kevin, The distribution of integers with a divisor in a given interval, Annals of Mathematics 168 (2008), 367-433.
Yong Hu, On the distribution of integers with divisors in two consecutive intervals, International Journal of Number Theory 9(4) (2013), 903-915.
doi:10.1142/s179304211350005x.
G. Bareikis and A. Maciulis, On the numbers of divisors in arithmetical semi- group, Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Comput. 39 (2013), 35-44.
M. S. Daoud, A. Hidri and M. Naimi, The distribution law of divisors on a sequence of integers, Lithuanian Math. J. 55(4) (2015), 474-488. doi:10.1007/s10986-015-9293-9
X. Wang and H. Guo, Distribution of RSA number’s divisor on T3 tree, International Journal of Information and Electronics Engineering 9(1) (2019), 23 29. doi: 10.18178/ijiee.2019.9.1.699.
Ford Kevin, Rough integers with a divisor in a given interval, J. Aust. Math. Soc. 111(1) (2021), 17-36. doi:10.1017/S1446788719000442.
Liubomir Chiriac, The average number of divisors in certain arithmetic sequences, Math. Pannon. (N. S.) 28 (2022), 136-142. doi: 10.1556/314.2022.00019.
Minkyu Kim and Jung Hee Cheo, Computing prime divisors in an interval, Math. Comp. 84(1) (2015), 339-354. doi: 10.1090/S0025-5718- 2014-02840-8.
L. Peng, Y. Lu, N. Kunihiro, R. Zhang and L. Hu, A deterministic algorithm for computing divisors in an interval, W. Susilo and G. Yang, eds., Information Security and Privacy, ACISP 2018, Lecture Notes in Computer Science, 10946, 2018. doi:10.1007/978-3-319-93638-3_1.
X. Wang, J. Li, Z. Duan and W. Wan, Probability to compute divisor of a hidden integer, Journal of Mathematics Research 10(1) (2018), 1-5.
doi:10.5539/jmr.v10n1p1.
X. Wang, Densification of witnesses for randomized algorithm design, Journal of Advances in Mathematics and Computer Science 38(10) (2023), 44-69.
doi: 10.9734/JAMCS/2023/v38i101823.
X. Wang, Frequently-used properties of the floor function, International Journal of Applied Physics and Mathematics 10(4) (2020), 135-142.
doi: 10.17706/ijapm.2020.10.4.135-142.
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