Alexander and Conway polynomials of Torus knots

We disprove the conjecture that if K is amphicheiral and K is concordant to K', then C_K'(z)C_K'(iz)C_K\(z²) is a perfect square inside the ring of power series with integer coefficients. The Alexander polynomial of (p,q)-torus knots are found to be of the form A_T(p,q)(t)= (f(t^q))/(f(t)) where f(t)=1+t+t²+...+t^p-1. Also, for (pⁿ,q)-torus knots, the Alexander polynomial factors into the form A_T(pⁿ ,q)=f(t)f(t^p)f(t^p2 )...f(t^pn-2 )f(t^pn-1 ). A new conversion from the Alexander polynomial to the Conway polynomial is discussed using the Lucas polynomial. This result is used to show that the Conway polynomial of (2ⁿ,q)-torus knots are of the form C_T(2ⁿ ,q)(z)=K₁K_2...K_n where K₁=F_q(z), F_q(z) being the Fibonacci polynomial, and K_i(z)=K_i-1(√z⁴+4z²).