Inspired by the recent work on $q$-congruences and the quadratic summation formula of Rahman, we provide some new $q$-supercongruences. By taking $qto 1$ in one of our results, we obtain a new Ramanujan-type supercongruence, which has the same right-hand side as Van Hammes (G.2) supercongruence for $pequiv 1 pmod 4$. We also formulate some related challenging conjectures on supercongruences and $q$-supercongruences.
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