Re: Finding n mod p^(D-1) given A=g^n mod p^D

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Tue, Apr 27, 2021 at 12:09:54PM +0300, Georgi Guninski wrote:
> We asked this on mathoverlow [1], but didn't get answer.
> 
> Let p be prime and n,g,D integers. Let A=g^n mod p^D
> 
> Let dlog(p,g,A,D)=log(A+O(p^D))/log(g+O(p^D)).
> 
> Conjecture 1: dlog(p,g,A,D) mod p^(D-1) = n mod p^(D-1)

Your function is not defined for all (p,g,A,D).
Otherwise this follows from the definition of the Iwasawa logarithm.

Cheers,
Bill