This paper proves infinite families of congruences modulo powers of 2 for overpartitions, indicating their deeper algebraic structure.
Recently, Hanson and Smith [7] proved Ramanujan type congruences modulo 3 for , where represents the number of overpartitions of with restricted odd differences. They also derived congruences modulo 5 for . In this paper, we prove several infinite families of congruences modulo powers of 2 for by employing -series identities and iterative computations.
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Guru et al. (2025) studied this question.
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