Abstract
In this paper, we investigate the arithmetic properties of bipartitions with 3-core. Let A3(n) denote the number of bipartitions with 3-core of n. We will prove one infinite family of congruences modulo 5 for A3(n). We also establish one surprising congruence modulo 14 for A3(8n+6). Finally, we prove that, if u(n) denotes the number of representations of a nonnegative integer n in the form x2+y2+3z2+3t2 with x,y,z,t∈Z, then u(6n+5)=12A3(2n+1).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
