Key points are not available for this paper at this time.
Let n>1 be an odd integer, and let be a primitive nth root of unity in the complex field. Via the Eigenvector-eigenvalue Identity, we show that ₃ (₍-₁) sign () ₉=₁^n-11+^j- (j) 1-^{j- (j) }= (-1) ^n-1{2} ( (n-2) !!) ²n, where D (n-1) is the set of all derangements of 1, , n-1. This confirms a previous conjecture of Z. -W. Sun. Moreover, for each =0, 1 we determine the value of +m₉₊₁ ₉, ₊ ₍-₁ completely, wherem₉₊=cases (1+^j-k) / (1-^j-k) &if\ j=k, \\&if\ j=k. cases
Wang et al. (Fri,) studied this question.