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CONGRUENCES MODULO LARGE POWERS OF 3 FOR 3ℓ-REGULAR CUBIC BIPARTITION

M. S. MAHADEVA NAIKA|S. Shivaprasada Nayaka
장전수학회 (Jangjeon Mathematical Society)|2020.07|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제23권 제3호|pp. 401-414|DOI 10.17777/pjms.2020.23.3.011

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키워드

Congruences3ℓ-regular cubic bipartitions
주제분류수학

초록

Let b3ℓ (n) denote the number of 3ℓ- regular cubic bipartition of n, where ℓ=1 and 2. In this paper, we establish some congruences modulo large powers 3 for b3ℓ (n). For example, for each α ≥ 0 and n ≥ 0, b3(32α+2n+32α+3+1/4)≡0 (mod 32α+2).

Abstract

Let b3ℓ (n) denote the number of 3ℓ- regular cubic bipartition of n, where ℓ=1 and 2. In this paper, we establish some congruences modulo large powers 3 for b3ℓ (n). For example, for each α ≥ 0 and n ≥ 0, b3(32α+2n+32α+3+1/4)≡0 (mod 32α+2).

참고문헌 (11)

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  6. M. D. Hirschhorn, "The Power of q, Developments in Mathematics, vol. 49" (2017), Springer
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  8. M. D. Hirschhorn, "A conjecture of B. Lin on cubic partition pairs", Ramanujan J, 45, pp.781~795 (2018)
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