Identifying checksum mechanisms using linear equations

Certain aspects of the present disclosure provide techniques for detecting errors in account numbers. One example method generally includes receiving, from a user device, an entered number associated with a user and determining, based on a first portion of the entered number, an entity associated with the entered number. The method further includes obtaining, from an account number database, a plurality of account numbers associated with the entity and generating, from the plurality of account numbers, an account number matrix. The method further includes attempting to solve a multiplication equation of the account number matrix, wherein a solution of the multiplication equation is a vector of constants, upon determining a solution to the multiplication equation, determining whether the entered vector is a valid number for the entity and upon determining the entered vector is a valid number for the entity, storing the entered number in the account number database.