# General congruences modulo 5 and 7 for colour partitions

@article{Saikia2021GeneralCM, title={General congruences modulo 5 and 7 for colour partitions}, author={Nipen Saikia and Chayanika Boruah}, journal={The Journal of Analysis}, year={2021}, pages={1-10} }

For any positive integers n and r , let $$p_r(n)$$ p r ( n ) denotes the number of partitions of n where each part has r distinct colours. Many authors studied the partition function $$p_r(n)$$ p r ( n ) for particular values of r . In this paper, we prove some general congruences modulo 5 and 7 for the colour partition function $$p_r(n)$$ p r ( n ) by considering some general values of r . To prove the congruences we employ some q -series identities which are also in the spirit of Ramanujan.

## 2 Citations

Arithmetic properties of 5-regular partition in three and five colours

- MathematicsThe Journal of Analysis
- 2022

Arithmetic properties for $$\ell $$-regular partition functions with distinct even parts

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- 2021

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