Karim Belabas on Sat, 11 Feb 2023 21:41:43 +0100

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Re: n-adic logarithms for composite n using Euler quotient.

* Georgi Guninski [2023-02-11 14:30]:
> First a question:  p-adic logarithm doesn't appear to work
> with composite moduli.

Pari's p-adics assume that p is prime (by design). To work with
"n-adics" for composite n, you will have to implement required
functions by hand, using integers and modular arithmetic.

>From the standard definition using inverse limits Z_n = \projlim_k Z / n^k Z
you get Z_n ~ \prod_{p | n, p prime} Z_p. Thus, depending on your application,
you might reduce to ordinary p-adics and CRT.


Pr Karim Belabas, U. Bordeaux, Vice-président en charge du Numérique
Institut de Mathématiques de Bordeaux UMR 5251 - (+33) 05 40 00 29 77