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If p is a prime and n a positive integer, let ν p (n) denote the exponent of p in n, and u p (n) = n/p νp(n) the unit part of n. If α is a positive integer not divisible by p, we show that the p-adic limit of (−1) pαe u p ((αp e)!) as e → ∞ is a well-defined p-adic integer, which we call z α,p. In terms of these, we then give a formula for the p-adic limit… (More)

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