How to "undo" mpz_invert()

[James Buchanan]

Sisyphus wrote:

> Not sure that I follow.
>
> mpz_invert(p, x, n) will set p to the inverse of x, modulo n. The 
> relationship can now be written:
> px = sn + 1
> and we're usually not interested in the value of s.
> Alternatively we say that px = 1 mod n.
>
> If you already have 'p' and you want to know what it's the inverse of, 
> then you simply:
> mpz_invert(p, p, n);
> and p will now be set to the value of x.
>
> Does that help ?

I have tried it with:

x = 12682271391376756984
n = 3527

Calculating the inverse modulo of x and n is:

p = 2288

Now I try to get x back by calculating the inverse modulo of n and p and 
get:
x = 2209

So what happened to the original big x?  Or is there some constant 
multiplier now that I must find so that 2209*k = the original x?

Cheers,
James