Kermit Rose <kermit@...> wrote:

> Suppose b0^p = 1 mod q, where q is prime.

...

> Let b = (b2 q^2 + b1 q + b0)

> Use formula for (b2 q^2 + b1 q + b0)^p to find

Get Pari-GP to do it for you :-)

> expansion mod q^3.

> If I were more familiar with that formula,

> I could do it here.

Assuming that p|q-1, with prime q,

we simply ask for

bsol(p,q)=lift(znprimroot(q^3)^(q^2*(q-1)/p));

\\ example:

b=bsol(5,11);if(Mod(b,11^3)^5==1,print(b));

1170

David