An easy proof of Ramanujan's famous congruences $p(5m+4)\equiv 0\equiv \ddot{I}„(5m+5)(\mathrm{mod}5)$

Hartosh Singh Bal, Gaurav Bhatnagar

We present a proof of Ramanujan's congruences $$p(5n+4)\equiv 0(\mathrm{mod}5)\text{ and }\ddot{I}„(5n+5)\equiv 0(\mathrm{mod}5).$$ The proof only requires a limiting case of Jacobi's triple produc…