Cubic partition pairs weighted by the parity of the crank
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Abstract
We study congruence properties of the number of cubic partition pairs weighted by the parity of the crank. If we define such number to be $c(n)$, then
\[
c(5n+4) \equiv 0 \pmod{5} \;\; \text{ and } \;\; c(7n+2) \equiv 0 \pmod{7},
\]
for all nonnegative integers $n$.
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References
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