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. 
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