SolveLinearCongruences.tex

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\begin{document}
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    \begin{algorithm}[H]
        \begin{algorithmic}
            \Require $R \in \mathbb{Z}^n, P \in (\mathbb{N}_{\geq 1})^n, n \in \mathbb{N}_{\geq 1}$, where \\
					$R$ is a vector with all rests $r_i$ and\\
					$P$ is a vector with all modulos $p_i$ such that\\
					($x \equiv r_i \mod p_i$) and $\left(i \neq j \Rightarrow \Call{gcd}{p_i, p_j} = 1 \right)$
			\\
			\State $M \gets \prod_{p \in P} p$

			\For{$i \in \{1, \dots, n\}$}
				\State $M_i \gets \frac{M}{p_i} $
				\State $y_i \gets \Call{getMultiplicativeInverse}{M_i, R_i}$
			\EndFor
            \\
            \State \Return $(\sum_{i=1}^n R_i y_i M_i, M)$
        \end{algorithmic}
    \caption{Solve a system of linear congruences}
    \label{alg:solveCongruences}
    \end{algorithm}
\end{preview}
\end{document}