Re: How to solve modular equations?

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

On Tue, Dec 28, 2021 at 07:09:20PM -0600, David Cleaver wrote:
> Is there a way to solve modular equations in pari-gp?
> 
> I've found how to solve simple modular equations with znlog, but how would
> I solve:
> A*10^(B*n) + C*n + D = 0 mod p
> where A, B, C, and D are integers and p is a prime.
> 
> For example, if A = 2, B = 2, C = -99, D = -9, and p = 13,
> how can I find which values of n are solutions to the equation?
> 
> For this example, I know that this function has solutions whenever n = [11,
> 19, 30] mod 39.
> 
> Is there a way to find general solutions like this?

For small p, it is easy:
First compute 
N = p*znorder(Mod(10,p)^B)
and try all n between 0 and N-1. 
This gives you all the solutions modulo N.

Cheers,
Bill.