CONGRUENCESFORBIPARTITIONSWITHODDDESIGNATED SUMMANDS

Authors

  • M.S.Mahadeva Naika DepartmentofMathematics, BengaluruCityUniversity, CentralCollegeCampus,Bengaluru-560001,Karnataka, INDIA
  • Harishkumar T DepartmentofMathematics, BengaluruCityUniversity, CentralCollegeCampus,Bengaluru-560001,Karnataka, INDIA
  • M. Prasad DepartmentofMathematics, PESCollegeofEngineering, Mandya-571401,Karnataka, INDIA
  • T.N. Veeranayaka DepartmentofMathematics, BengaluruCityUniversity, CentralCollegeCampus,Bengaluru-560001,Karnataka, INDIA

DOI:

https://doi.org/10.56827/SEAJMMS.2023.1902.01

Abstract

Andrews, Lewis andLovejoy investigatedanewclass of partitions withdesignatedsummandsbytakingordinarypartitionsandtaggingexactlyone ofeachpartsize.LetB2(n)countthenumberofbipartitionsofnwithdesignated summands inwhichall partsareodd. Inthiswork,weestablishmany infinite familiesofcongruencesmodulopowersof2and3forB2(n).Forexample, foreach n≥0andα≥0, B2 48·52α+2n+a1·52α+1 ≡0 (mod9), wherea1∈{88,136,184,232}.

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Published

2023-08-30

Issue

Vol. 19 No. 02 (2023): South East Asian Journal of Mathematics and Mathematical Sciences

Section

Articles