Factors of certain basic hypergeometric sums (Q6200982)

Let \( \Phi_n(q)\) be the \(n\)-th cyclotomic polynomial in \(q\), which can be factorized as \[ \prod_{\substack{ 1\le k\le n \\ \gcd(k,n)=1}} (q-\zeta^k), \] where \(\zeta\) is an \(n\)-th primitive root of unity. The authors study certain truncated basic hypergeometric series containing the factor \( \Phi_n(q)\). Their main result may be considered a generalisation of Theorem 1.1 in [\textit{V. J. W. Guo}, J. Math. Anal. Appl. 476, No. 2, 851--859 (2019; Zbl 1448.33016)].