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To calculate the horizontal position, the kinematic differential
equations are needed:
\begin{align}
\dot{n} &= u\cos\psi -v\sin\psi \\
\dot{e} &= u\sin\psi + v\cos\psi
\end{align}
For small angles the following approximation can be used:
\begin{align}
\dot{n} &= u -v\delta_\psi \\
\dot{e} &= u\delta_\psi + v
\end{align}
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Fermat's Last Theorem states that
\begin{align}
x^n + y^n = z^n
\end{align}
has no non-zero integer solutions for $x$, $y$ and $z$ when $n > 2$.
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