In a recent paper, Wang [1981] introduces a p-adic algorithm for the construction of partial fraction decompositions. This differs from the usual p-adic algorithms for factorisation or the computation of greatest common divisors ([Wang, 1978], [Wang, 1980], [Moore & Norman, 1981]) in that the p-adic image is used to reconstruct rational numbers, rather than integers.
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Wang et al. (1982) studied this question.