Geodesic
Two infinite families of congruences modulo 9 for overcubic partition pairs
Bernard Lishuang Lin1 ; Erin Yiying Shen2 ; Andrew Yezhou Wang3
1School of Science Jimei University 361021 Xiamen, P.R. China
2School of Sciences Hohai University 210098 Nanjing, P.R. China
3School of Mathematical Sciences University of Electronic Science and Technology of China 611731 Chengdu, P.R. China
Colloquium Mathematicum, Tome 147 (2017) no. 1, pp. 115-123
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Let $\overline {b}(n)$ denote the number of overcubic partition pairs of $n$. Applying the theory of modular forms, Kim obtained two congruences for $\overline {b}(n)$ modulo $3$ and $64$. More congruences modulo $3$ and $5$ have been found by the first author of the present paper. In this paper, we proceed with the study of the congruence properties of $\overline {b}(n)$ and establish two infinite families of congruences modulo $9$.
DOI : 10.4064/cm6843-4-2016
Keywords: overline denote number overcubic partition pairs applying theory modular forms kim obtained congruences overline modulo congruences modulo have found first author present paper paper proceed study congruence properties overline establish infinite families congruences modulo nbsp

Bernard Lishuang Lin  1   ; Erin Yiying Shen  2   ; Andrew Yezhou Wang  3

1 School of Science Jimei University 361021 Xiamen, P.R. China
2 School of Sciences Hohai University 210098 Nanjing, P.R. China
3 School of Mathematical Sciences University of Electronic Science and Technology of China 611731 Chengdu, P.R. China 
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Bernard Lishuang Lin; Erin Yiying Shen; Andrew Yezhou Wang. Two infinite families of congruences modulo 9 for overcubic partition pairs. Colloquium Mathematicum, Tome 147 (2017) no. 1, pp. 115-123. doi: 10.4064/cm6843-4-2016

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