Abstract：Based on the knot theory, this paper shows that (m2-1)(n2-1)，(m-1)(n-1)(2mn-m-n-1) are divisible by 24 and 12,respectively, by using the properties of the second derivatives of the Jones polynomial and Alexander polynomial of T(m, n) and that m, n must be coprime for Torus knot T(m, n).
陶志雄. 纽结理论在数论中的应用[J]. 浙江大学学报（理学版）, 2020, 47(3): 312-314.
TAO Zhixiong. An application of knot theory in number theory. Journal of ZheJIang University(Science Edition), 2020, 47(3): 312-314.
1 潘承洞，潘承彪. 初等数论 [M]. 北京：北京大学出版社，2003. PAN C D, PAN C B. Elementary Number Theory [M]. Beijing: Beijing University Press, 2003. 2 JONES V F R. Hecke algebra representations of braid groups and link polynomials [J]. Annals of Math, 1987,126:335-388.DOI:10.1142/9789812798329_0003 3 KAUFFMAN L H. On Knots [M]. Beijing: World Publishing Corporation (Princeton University Press) 1990. 4 BURDE G, ZIESCHANG H. Knots [M]. Berlin/ New York: Walter de Gruyter,1985. 5 KAWAUCHI A. A Survey of Knot Theory [M]. Basel/Boston/Berlin: Birkh?user, 1996. DOI:10.1007/978-3-0348-9227-8 6 HOSTE J. The Arf invariant of a totally proper link [J]. Topology Appl,1985,18:163-177.DOI:10.1016/0166-8641(84)90008-7 7 ADAMS C C. The Knot Book [M]. New York: W H Freeman and Company, 2004. DOI:10.2307/3618337 8 陶志雄. Jones多项式的一个赋值性质 [J]. 浙江大学学报（理学版），2014, 41(5)：509-511.DOI:10.3785/j.issn.1008-9497.2014.05.005 TAO Z X. An evaluation property of Jones polynomial of a link [J]. Journal of Zhejiang University (Science Edition), 2014, 41(5): 509-511.DOI:10.3785/j.issn.1008-9497.2014.05.005
2020, Vol. 47 
