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We establish two binomial coefficient--generalized harmonic sum identitiesusing the partial fraction decomposition method. These identities are a keyingredient in the proofs of numerous supercongruences. In particular, in otherworks of the author, they are used to establish modulo $p^k$ ($k>1$)congruences between truncated generalized hypergeometric series, and a functionwhich extends Greene's hypergeometric function over finite fields to the$p$-adic setting. A specialization of one of these congruences is used to provean outstanding conjecture of Rodriguez-Villegas which relates a truncatedgeneralized hypergeometric series to the $p$-th Fourier coefficient of aparticular modular form.

Binomial coefficient-harmonic sum identities associated to supercongruences