A note on probabilistically verifying integer and polynomial products

Probabilistic algorithms are presented for testing the result of the product of two <italic>n</italic>-bit integers in <italic>O</italic>(<italic>n</italic>) bit operations and for testing the result of the product of two polynomials of degree <italic>n</italic> over <italic>any</italic> integral domain in 4<italic>n</italic> + <italic>o</italic>(<italic>n</italic>) algebraic operations with the error probability <italic>o</italic>(l/<italic>n</italic><supscrpt>1-ε</supscrpt>) for any ε > 0. The last algorithm does not depend on the constants of the underlying domain.