Let M be set of positive integers. A sequence s(n) satisfies a supercongruence for M if for every m in M the sequence s(m) mod m is ultimately periodic. s(n) is MC-finite if M=\mathbb{N}. We discuss how to prove supercongruences and give various applications to integer sequences.

Joint work with Y. Filmus, E. Fischer and V. Rakita.

(Published as: MC-finiteness of restricted set partition functions, Journal of Integer sequences, vol. 26 (2023) Article 23.7.4)