Two $q$-congruences from Jackson's ${}_8{\phi }_7$ summation and Andrews' ${}_4{\phi }_3$ summation

We prove two $q$-congruence conjectures of Guo on truncated basic hypergeometric series. The first result strengthens a congruence obtained from Jackson’s terminating very-well-poised ${}_8{\phi }_7$ summation from the modulus ${\mathrm{\Phi }}_n(q{)}^4$ to the modulus ${\mathrm{\Phi }}_n(q{)}^5$ when $n\equiv 3(\mathrm{m}\mathrm{o}\mathrm{d}5)$. The second result proves a cyclotomic congruence modulo ${\mathrm{\Phi }}_n(q)$ when $n\equiv 1(\mathrm{m}\mathrm{o}\mathrm{d}4)$, by a specialization of Andrews’ terminating ${}_4{\phi }_3$ summation.