Key points are not available for this paper at this time.
One variant of the q-Catalan polynomials is defined in terms of Gaussian polynomials by Cₖ (q) =0pt2kkq-q0pt2kk+1q. Liu studied congruences of the form ₊=₀^n-1 qᵏCₖ modulo the cyclotomic polynomial ₙ (q) ², provided that n 13. Apparently the case n 03 has been missing from the literature. It is our primary purpose to fill this gap by the current work. In addition, we discuss certain fascinating link to Dirichlet character sum identities.
Amdeberhan et al. (Tue,) studied this question.