Melham conjectures 21 identities, all of which are analogous to Jacobi’s two-square theorem. A small number of these have already been proved in various ways by other authors, and in 2013 Toh proved all of them using similar, known identities. In this paper we o?er an alternative and straightforward method to proving all of them using the theory of modular forms, in particular, Sturm’s bound, which we explain in detail.
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