Keywords and phrases: Mersenne prime, elliptic curve.
Received: August 7, 2022; Accepted: September 14, 2022; Published: November 28, 2022
How to cite this article: Shin-Wook Kim, Mersenne prime’s function in elliptic curves and , JP Journal of Algebra, Number Theory and Applications 59 (2022), 47-66. http://dx.doi.org/10.17654/0972555522038
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] C. Caldwell, http://primes.utm.edu/curios/includes/primetest.php. [2] S.-W. Kim and H. Park, Range of rank in an elliptic curve, Far East J. Math. Sci. (FJMS) 74(2) (2013), 379-388. [3] S.-W. Kim, Ranks of elliptic curves Int. J. Algebra 9(5) (2015), 205-211. http://dx.doi.org/10.12988/ija.2015.5421. [4] S.-W. Kim, Various forms in components of primes, Int. J. Algebra 13(2) (2019), 59-72. https://doi.org/10.12988/ija.2019.913. [5] S.-W. Kim, Enumeration in ranks of various elliptic curves Int. J. Algebra 14(3) (2020), 139-162. https://doi.org/10.12988/ija.2020.91250. [6] S.-W. Kim, Ranks in elliptic curves with varied primes, Int. J. Cont. Math. Sci. 15(3) (2020), 127-162. https://doi.org/10.12988/ijcms.2020.91442. [7] S.-W. Kim, Multi exponent of coefficient in elliptic curves, Far East J. Math. Sci. (FJMS) 126(2) (2020), 121-133. [8] S.-W. Kim, Ranks in some elliptic curves JP Journal of Algebra, Number Theory and Applications 51(2) (2021), 223-248. [9] S.-W. Kim, Ranks in elliptic curves of the forms Int. J. Algebra 16(3) (2022), 109-218. https://doi.org/10.12988/ija.2022.91726. [10] F. Lemmermeyer, Reciprocity Laws, Springer, 2000. [11] P. Ribenboim, Algebraic Numbers, Wiley-Interscience, 1972. [12] J. H. Silverman and J. Tate, Rational Points on Elliptic Curves, Springer, New York, 1992. http://dx.doi.org/10.1007/978-1-4757-4252-7. [13] B. K. Spearman, On the group structure of elliptic curves Int. J. Algebra 1(5) (2007), 247-250. [14] https://en.wikipedia.org/wiki/Mersenne-prime.
|