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Abstract for 
Michael Hirschhorn and James A. Sellers,
Two Congruences Involving 4-cores

The goal of this paper is to prove two new congruences involving
4--cores using elementary techniques; namely, if $a_4(n)$ denotes the
number of 4--cores of $n$, then $a_4(9n+2)\equiv 0$ (mod 2)
and $a_4(9n+8)\equiv 0$ (mod 4).






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