Proof of a conjecture of Andrews and El Bachraoui on the parity of two-color partitions
Abstract
In this paper, we prove a conjecture of Andrews and El Bachraoui concerning the parity of certain two-color partitions. Precisely, we show that if the Fourier coefficient to(n) of the corresponding q-series is odd, then 8n+9 is represented by the binary quadratic form x2+2y2.
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