Theoretical analysis reveals new congruences for central factorial and Euler numbers, highlighting connections to classical identities from Ramanujan and Hardy.
Our present investigation is motivated essentially by important contributions by Srinivasa Ramanujan (1887–1920) and Godfrey Harold Hardy (1877–1947) on various classes of identities involving congruences and modular equations. Here, in this paper, we prove several congruences for the central factorial numbers and the Euler numbers. Relevant connections with some of the known results on this subject are also indicated.
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Liu et al. (2026) studied this question.
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