Fault-Tolerant Modular Reconstruction of Rational Numbers

In this paper we present two efficient methods for reconstructing a rational number from several residue-modulus pairs, some of which may be incorrect. One method is a natural generalization of that presented by Wang, Guy and Davenport in \cite{WGD1982} (for reconstructing a rational number from $\mathit{\text{correct}}$ modular images), and also of an algorithm presented in \cite{Abb1991} for reconstructing an $\mathit{\text{integer}}$ value from several residue-modulus pairs, some of which may be incorrect.