On determinants involving tangent functions.

In this paper, we study certain determinants involving tangent functions. We prove that for any odd number n ⩾ 3 and s ∈ Z + , the determinant D (n , s) = det (tan s ⁡ π j + k n) 1 ⩽ j , k ⩽ n − 1 ∈ n n − 2 Z . In the special case s = 2, we confirm a conjecture raised by Zhi-Wei Sun in 2019. [ABSTRACT FROM AUTHOR]