This paper presents a fault-tolerant technique based on the modulus replication residue number system (MRRNS) which allows for modular arithmetic computations over identical channels. In this system, fault tolerance is provided by adding extra computational channels that can be used to redundantly compute the mapped output. An algebraic technique is used to determine the error position in the mapped outputs and provide corrections. We also show that by taking advantage of some elementary polynomial properties we obtain the same level of fault tolerance with about a 30% decrease in the number of channels. This new system is referred to as the symmetric MRRNS (SMRRNS).