Infinite Families of Congruences Modulo 5 for Ramanujan's General Partition Function

14 Aug 2020  ·  Saikia Nipen, Chetry Jubaraj ·

For any non-negative integer $n$ and non-zero integer $r$, let $p_r(n)$ denote Ramanujan's general partition function. By employing $q$-identities, we prove some new Ramanujan-type congruences modulo 5 for $p_r(n)$ for $r=-(5\lambda+1), -(5\lambda+3), -(5\lambda+4), -(25\lambda+1)$, $-(25\lambda+2)$, and any integer $\lambda$...

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Number Theory