NAME: Rhiannon Weaver                 

ADDRESS: 204 Atherton Hall          
         University Park, Pa                   
         16802
       

EMAIL ADDRESS: rlw146@psu.edu     

TITLE OF TALK: New Congruences for the Partition Function            

ABSTRACT OF TALK: 
Let $p(n)$ be the number of unrestricted partitions of a non-negative integer 
$n$.  Ramanujan proved for all $n \ge 0$ that
\begin{align}
 p(5n+4) &\equiv  0 \pmod{5}, \\
 p(7n+5) &\equiv  0 \pmod{7}, \\
 p(lln+6) &\equiv 0 \pmod{11}.
\end{align}
Recently, Ono proved for every prime $\ge$ 5 that there exist infinitely many
congruences of the type $p(An+B) \equiv 0 \pmod{m}$.  However, his results are
theoretical and do not lead to an effective algorithm for finding such
congruences.  Here we obtain such an algorithm for primes $13 \le m \le 31$
which reveals 70,266 new congruences.
 
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