纽结理论在数论中的应用

An application of knot theory in number theory.

基于纽结理论,利用Torus纽结T(m,n)(m,n须为互素)及Jones多项式和Alexander多项式在二阶导数下的性质,证明了(m^2-1)(n^2-1),(m-1)(n-1)(2mn-m-n-1)可分别被24与12整除。

Based on the knot theory,this paper shows that(m^2-1)(n^2-1),(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).