  Using Dwork's theory, we prove a broad generalisation of his famous p-adic
formal congruences theorem. This enables us to prove certain p-adic congruences
for the generalized hypergeometric series with rational parameters; in
particular, they hold for any prime number p and not only for almost all
primes. Along the way, using Christol's functions, we provide an explicit
formula for the "Eisenstein constant" of any globally bounded hypergeometric
series with rational parameters. As an application of these results, we obtain
an arithmetic statement of a new type concerning the integrality of Taylor
coefficients of the associated mirror maps. It essentially contains all the
similar univariate integrality results in the litterature.
