FAMILY OF CONGRUENCES FOR (2, ?)?REGULAR BIPARTITION TRIPLES
Bipartition Triples; Congruences; Integer partitions; q?series
Though congruences have their limitations, they have significant importance in the field of number theory and helps in proving many interesting results. Thus, this article has adopted the technique and properties of congruences to identify and prove a set of congruent properties for integer partition. The partition of a positive integer is a way of expressing the number as a sum of positive integers. One such partitions known as regular bipartition triple are discussed in this article. New congruences modulo even integers and modulo prime (p ? 5) powers are derived for (2, ?)?regular bipartition triples. Also infinite families of congruences modulo 2 for some (2, ?)?regular bipartition triples are derived. The theorems stated in this article are proved using the q?series notation and some of the prominent results such as Eulers pentagonal number theorem and Jacobis triple product identities. There are certain lemmas which are derived using these results that help in proving the major results of this article. 2022, RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES. All rights reserved.
South East Asian Journal of Mathematics and Mathematical Sciences, Vol-18, No. 3, pp. 1-14.
RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES
https://doi.org/10.56827/SEAJMMS.2022.1803.1 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85165894676&doi=10.56827%2fSEAJMMS.2022.1803.1&partnerID=40&md5=92c2bf760d05d1daccdbc8f5b4edcf70
Puneeth V., Department of Computational Sciences, CHRIST University, Bengaluru, 560029, India; Roy A., Department of Sciences and Humanities, CHRIST University, Bengaluru, 560029, India