Speeding up RSA signature authentication is important in various scenarios. We propose here a scheme for quick verification of RSA signatures, that is mostly appropriate when the public exponent is small. This scheme pre-computes the quotients required to perform modular reduction during verification, and includes them as part of the certificate that is being authenticated. This allows for replacing expensive modular reduction steps by less costly integer multiplications and subtractions. As a result, the scheme achieves significant speedup as well as reduction in the code size and complexity. The quotients are computed using only the public key and the signature, and do not need to involve the signing procedure, nor require any changes in it. The verification scheme that uses these quotients as part of a quick verification flow is no weaker than the cryptographic primitive on which the signature scheme is based. The performance results that are reported in the paper demonstrate the advantage of the proposed scheme.