A supercongruence is a congruence between rational numbers modulo a power of a prime. In this paper, we give a technique for finding and algorithmically proving supercongruences by expressing terms as infinite series involving certain generalizations of the harmonic numbers. We apply the technique to derive many new supercongruences. We also provide software for finding and proving supercongruences using our technique.
The present work involves infinite, @math -adically convergent series identities involving multiple harmonic sums, and in Section we look at related series involving truncated multiple polylogarithms. A recent work of Seki @cite_6 investigates a closely related @math -adic series identity for truncated multiple polylogarithms.
@cite_6
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We prove the @math -adic duality theorem for the finite star-multiple polylogarithms. That is a generalization of Hoffman's duality theorem for the finite multiple zeta-star values.