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Plus, Command and Conquer: Red Alert 3-On-The-Mac features a directÂ .
Ø Mac OS X. Command and Conquer: Red Alert 3 is out today, and you can download it fromÂ .
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If you are interested in the Windows version of Red Alert 3, for example, I would recommend downloadingÂ .Q:

solving system of Pell’s equation

I am trying to solve $19^x + 9^y = 82 \mod p$ where $p$ is a prime number and $x, y \in \mathbb{Z}$.
From the comments below my previous question (solving Pell’s equation with Bézout’s identity and Hacker’s method), I have found there is a quadratic relation between $x$ and $y$.
If $\bar{u} = (u, v)$ is the vector of $u$ and $v$, then I have found
$$(x, y) = (u, v) A^{ -1} = T_p(19^x, 9^y)$$
where $A = \begin{pmatrix}82 & 19\\9 & 1\end{pmatrix}$ is the matrix of $T_p$ of rank 2 and it has no repeated eigenvalues.
By the way, $T_p$ is the transformation that induces a linear recursion between $x$ and $y$, and the recursion is not polynomial. So I am looking for the general solution of $19^x + 9^y = 82 \mod p$ (for all primes $p$). Is it possible? Thanks in advance.
EDIT: $T_p$ is the matrix induced by
$$(u, v) \begin{pmatrix}19 & 82\\9 & 1\end{pmatrix}^{ -1} = (T_p(u, v), T_p(19 u, 2 v))$$

Your matrix $T_p$ is not going to work. It is not invertible since it has repeated eigenvalues $\lambda=1$ and $\lambda=82$ and therefore eigenvalues which
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“Commander Christian, he’d been a good man, in the way that was possible for one so fair. He’d kept the worst of the War Crimes Trials to the end. Right up to the last. Quite a few of the lesser ones, the ones looking most like a danger, had been shipped to the mines here.” Chapter Ten: “The Square Has a Name”

“An obvious ship has been seen in orbit in the area. A tall woman has been seen at the spaceport who fits the profile of a possible State Department operative but there’s been no talk of an arrest. Darruthers and his party, the “White Rose”, (headline of their paper) have printed their response to the State and the Philosophers’ Collective: “We Are All Germinating Seeds.” Four of them have been detained and moved to the mines. There have been rumours, unconfirmed by either side, that their trial will be meted out by a new Revolutionary Tribunal. ”

“The city has increased its expenditure on the censorship of the rumours in the media. Their physical protection is just now being considered.” Chapter Eleven: “On the Face of Things”

“Liu is buying bodies in the suburbs and turning them into members of the Anarchist Party. According to the new tax, he’s also farming out his workers, who are being made to work the land on illegal plots. If the State bothers to try and stop him it’s just playing into his hands. And if he can manage