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Such congruences, those of the form $p_{-t}(\\ell n + a) \\equiv 0 \\pmod {\\ell}$, were previously studied by Kiming and Olsson. If $\\ell \\geq 5$ is prime and $-t \\not \\in \\{\\ell - 1, \\ell -3\\}$, then such congruences satisfy $24a \\equiv -t \\pmod {\\ell}$. Inspired by Lin's example, we obtain natural infinite families of such congruences. 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In analogy with Ramanujan's work on the partition function, Lin recently proved in \\cite{Lin} that $p_{-3}(11n+7)\\equiv0\\pmod{11}$ for every integer $n$. Such congruences, those of the form $p_{-t}(\\ell n + a) \\equiv 0 \\pmod {\\ell}$, were previously studied by Kiming and Olsson. If $\\ell \\geq 5$ is prime and $-t \\not \\in \\{\\ell - 1, \\ell -3\\}$, then such congruences satisfy $24a \\equiv -t \\pmod {\\ell}$. Inspired by Lin's example, we obtain natural infinite families of such congruences. 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