Ramanujan type of congruences modulo m for (l, m)-regular bipartitions

Kathiravan, T.

doi:10.48550/arxiv.1907.13450

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2019

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“…a(q 3 )f 3 − 3f 3 9 q f 6 3 f 9 +16qf 15 3 f 9 , ≡ 16qf 15 3 f 9 + 6qa(q 3 ) 3 f 6 3 f 4 9 + 8q 4 f 3 3 f 13 9 .…”

Section: It Follows Thatunclassified

Some congruences for $(s,t)$-regular bipartitions modulo $t$

Kathiravan¹,

Srilakshmi²

2019

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In this work, we study the function B s,t (n), which counts the number of (s, t)-regular bipartitions of n. Recently, many authors proved infinite families of congruences modulo 11 for B 3,11 (n), modulo 3 for B 3,s (n) and modulo 5 for B 5,s (n). Very recently, Kathiravan proved several infinite families of congruences modulo 11, 13 and 17 for B 5,11 (n), B 5,13 (n) and B 81,17 (n). In this paper, we will prove infinite families of congruences modulo 5 for B 2,15 (n), modulo 11 for B 7,11 (n), modulo 11 for B 27,11 (n) and modulo 17 for B 243,17 (n) .

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“…a(q 3 )f 3 − 3f 3 9 q f 6 3 f 9 +16qf 15 3 f 9 , ≡ 16qf 15 3 f 9 + 6qa(q 3 ) 3 f 6 3 f 4 9 + 8q 4 f 3 3 f 13 9 .…”

Section: It Follows Thatunclassified