Ramanujan-Like Congreuences of the Distinct Partition Function

Authors

Ian Blumenfeld
Christi Carlstead
Mimi Cukier
Wesley Terway

Document Type

Article

Publication Date

12-30-2000

First Advisor

John Rickert

Abstract

In his work with the partition function, Ramanujan observed several congruences of the form p(An + B) = 0 (mod m). We adapt this form to several congruences of the distinct partition function, p2(n). We show that one can determine all ordered pairs of integers (A;B) for which p₂(An + B)=0 (mod 2) and show families of congruences modulo 4. Finally, we offer a proof of a congruence modulo 5 satisfied by the distinct partition function.

Comments

MSTR 00-11

Recommended Citation

Blumenfeld, Ian; Carlstead, Christi; Cukier, Mimi; and Terway, Wesley, "Ramanujan-Like Congreuences of the Distinct Partition Function" (2000). Mathematical Sciences Technical Reports (MSTR). 106.
https://scholar.rose-hulman.edu/math_mstr/106