Can anyone help me with this modular manipulation in system of equations? So i have to solve this system but i got stuck while computing and I need help.
m = 928377461;
x0 = 21380413;
x1 = 32564732;
x2 = 803330610;
a*x0+c === x1 mod m
a*x1+c === x2 mod m

I know the x's and m but I can't figure out reasonable equation to get a and c, because they have to be integers.
I considered:
a = ((x1 - (x1 * x1) - (x2 * x0)) / (x1 - x0)) mod m
c = (((x1 * x1) - (x2 * x0)) / (x1 - x0)) mod m

But they are not giving correct result (It's taken from linear congruential generator).
I would be really thankful if anyone could give me the correct formulas, cause i don't have a clue how am i supposed to solve it and everywhere i searched this part was described as a basic arithmetics, which seems to be too hard for me.
 A: Hint:
From the two congruence equations, you can eliminate $c$ to obtain
$$a(x_1-x_0)\equiv x_2-x_1\pmod m.$$
Next, supposing $x_1-x_0$ is coprime to $m$, it has a modular inverse that you can find with the extended Euclidean algorithm. Multiplying both sides by this modular inverse will give you the congruence class of $a$. Then it is easy to deduce the congruence class of $c$.
Here is how it starts:
$x_1-x_0=11\,184\,319$
\begin{array}{rrrl}
r_i\qquad&u_i&v_i&q_i\\\hline
m=928\,377\,461&0&1\\
x_1-x_0=11\,184\,319&1&0&83\\\hline
78\,984&-83&1&1 \\
47\,575 & 84&-1&1\\
31\,409&-167&2&1\\
16\,166&251&-3&1\\
\vdots\quad&\vdots\enspace&\vdots\,&\vdots\end{array}
A: Ooookay...
$x_2 - x_1 \equiv ax_1 - ax_0 \equiv a(x_1-x_0)\pmod m$.
If $\gcd(x_1-x_0, m) =1$ then $x_1-x_0$ is invertible. So
$a \equiv (x_2 - x_1)(x_1-x_0)^{-1} \pmod m$
And the $c \equiv x_1-ax_0 \pmod m$.
So...
$x_1-x_0 = 11184319$ now use Euclid's Algorithm to find $\gcd(x_1-x_0, m)$ and solve $(x_1-x_0)^{-1}$.
$m = 928377461$
$928377461= 83*11184319 + 78984$
$11184319 = 141*78984+ 47575$ etc....
