Theoretical analysis uncovers new modular congruences for regular bipartitions using continued fractions, highlighting deeper divisibility properties in partition theory.
For any positive integer ℓ , B_ (n) B ℓ ( n ) represents the number of ℓ -regular bipartitions of n . By employing q -series identities and Rogers−Ramanujan continued fraction identities, we establish new congruences for ℓ = 8, 9, 16, 32 and 35 under modulo 2, 3, and 7.
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Maheshagouda et al. (2026) studied this question.
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