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So I know that it can proved via modular forms by expressing the discriminant function in terms of the Eisenstein series $E_4^3$ and $E_12$ and reducing the equation using mod 691 (twice)

But this wasn't the original proof right? Did the original proof use elementary number theory? what year was it proved?

Modular forms simplifies the proof somewhat right?

Many thanks

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    Might be a better fit at http://hsm.stackexchange.com/ – 2017-01-22
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    The [Ramanjuan conjecture](https://en.wikipedia.org/wiki/Ramanujan_tau_function#Ramanujan.27s_conjectures) is about the bound $\tau(p) = \mathcal{O}(p^{11/2})$ which is better than the more trivial [cusp form bound](http://mathoverflow.net/a/43951/84768) $\tau(p) = \mathcal{O}(p^{12/2})$. How the congruence $\tau(n) \equiv \sigma_{11}(n) \bmod 691$ is related to it ? – 2017-01-22
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    It would be most helpful if you could include in your question the statement/conjecture which you are talking about... – 2017-01-22
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    The [original paper](http://ramanujan.sirinudi.org/Volumes/published/ram18.pdf) is online. The "real" reason for the congruence is that the mod $691$ Galois representation attached to $\Delta$ is reducible. [This question](https://math.stackexchange.com/questions/154593/ramanujan-691-congruence?rq=1) gives an overview of this approach. – 2017-01-24

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